List of publications

List of publications
J. Grabowski
January 27, 2017
References
[1] Andrew James Bruce, Katarzyna Grabowska, and Janusz Grabowski. Linear duals of
graded bundles and higher analogues of (Lie) algebroids. J. Geom. Phys., 101:71–99,
2016.
[2] Andrew James Bruce, Janusz Grabowski, and Mikolaj Rotkiewicz. Polarisation of graded
bundles. SIGMA Symmetry Integrability Geom. Methods Appl., 12:Paper No. 106, 30,
2016.
[3] J. F. Cariñena, F. Falceto, and J. Grabowski. Solvability of a Lie algebra of vector fields
implies their integrability by quadratures. J. Phys. A, 49(42):425202, 13, 2016.
[4] Tiffany Covolo, Janusz Grabowski, and Norbert Poncin.
supermanifolds. J. Math. Phys., 57(7):073503, 16, 2016.
[5] Tiffany Covolo, Janusz Grabowski, and Norbert Poncin.
supermanifolds. J. Geom. Phys., 110:393–401, 2016.
The category of Zn2 -
Splitting theorem for Zn2 -
[6] Andrew James Bruce, Katarzyna Grabowska, and Janusz Grabowski. Graded bundles
in the category of Lie groupoids. SIGMA Symmetry Integrability Geom. Methods Appl.,
11:Paper 090, 25, 2015.
[7] Andrew James Bruce, Katarzyna Grabowska, and Janusz Grabowski. Higher order mechanics on graded bundles. J. Phys. A, 48(20):205203, 32, 2015.
[8] J. F. Cariñena, F. Falceto, J. Grabowski, and M. F. Rañada. Geometry of Lie integrability
by quadratures. J. Phys. A, 48(21):215206, 18, 2015.
[9] J. F. Cariñena, J. Grabowski, J. de Lucas, and C. Sardón. Dirac-Lie systems and
Schwarzian equations. J. Differential Equations, 257(7):2303–2340, 2014.
[10] Janusz Grabowski, Katarzyna Grabowska, and Pawel Urbański. Geometry of Lagrangian
and Hamiltonian formalisms in the dynamics of strings. J. Geom. Mech., 6(4):503–526,
2014.
[11] Janusz Grabowski. Modular classes revisited.
11(9):1460042, 11, 2014.
Int. J. Geom. Methods Mod. Phys.,
[12] Katarzyna Grabowska and Janusz Grabowski. Tulczyjew triples: from statics to field
theory. J. Geom. Mech., 5(4):445–472, 2013.
[13] Janusz Grabowski. Brackets. Int. J. Geom. Methods Mod. Phys., 10(8):1360001, 45, 2013.
1
[14] Janusz Grabowski and Javier de Lucas. Mixed superposition rules and the Riccati hierarchy. J. Differential Equations, 254(1):179–198, 2013.
[15] Janusz Grabowski. Graded contact manifolds and contact Courant algebroids. J. Geom.
Phys., 68:27–58, 2013.
[16] Janusz Grabowski, Alberto Ibort, Marek Kuś, and Giuseppe Marmo. Convex bodies of
states and maps. J. Phys. A, 46(42):425301, 18, 2013.
[17] Janusz Grabowski, David Khudaverdyan, and Norbert Poncin. The supergeometry of
Loday algebroids. J. Geom. Mech., 5(2):185–213, 2013.
[18] Janusz Grabowski, Alexei Kotov, and Norbert Poncin. Lie superalgebras of differential
operators. J. Lie Theory, 23(1):35–54, 2013.
[19] J. F. Cariñena, J. Grabowski, and J. de Lucas. Superposition rules for higher order systems
and their applications. J. Phys. A, 45(18):185202, 26, 2012.
[20] Janusz Grabowski, Marek Kuś, and Giuseppe Marmo. Segre maps and entanglement for
multipartite systems of indistinguishable particles. J. Phys. A, 45(10):105301, 17, 2012.
[21] Janusz Grabowski. Modular classes of skew algebroid relations. Transform. Groups,
17(4):989–1010, 2012.
[22] Janusz Grabowski and Mikolaj Rotkiewicz. Graded bundles and homogeneity structures.
J. Geom. Phys., 62(1):21–36, 2012.
[23] Katarzyna Grabowska and Janusz Grabowski. Dirac algebroids in Lagrangian and Hamiltonian mechanics. J. Geom. Phys., 61(11):2233–2253, 2011.
[24] Janusz Grabowski and Michal Jóźwikowski. Pontryagin maximum principle on almost Lie
algebroids. SIAM J. Control Optim., 49(3):1306–1357, 2011.
[25] Janusz Grabowski, Alexei Kotov, and Norbert Poncin. Geometric structures encoded in
the Lie structure of an Atiyah algebroid. Transform. Groups, 16(1):137–160, 2011.
[26] Janusz Grabowski, Marek Kuś, and Giuseppe Marmo. Entanglement for multipartite
systems of indistinguishable particles. J. Phys. A, 44(17):175302, 21, 2011.
[27] Remigiusz Augusiak, Janusz Grabowski, Marek Kuś, and Maciej Lewenstein. Searching
for extremal ppt entangled states. Optics Communications, 283(5):805–813, 2010.
[28] José F. Cariñena, Janusz Grabowski, and Javier de Lucas. Lie families: theory and
applications. J. Phys. A, 43(30):305201, 18, 2010.
[29] Janusz Grabowski, Alexei Kotov, and Norbert Poncin. The Lie superalgebra of a supermanifold. J. Lie Theory, 20(4):739–749, 2010.
[30] Janusz Grabowski, Pawel Urbański, and Mikolaj Rotkiewicz. Double affine bundles. J.
Geom. Phys., 60(4):581–598, 2010.
[31] José F. Cariñena, Janusz Grabowski, and Javier de Lucas. Quasi-Lie schemes: theory and
applications. J. Phys. A, 42(33):335206, 20, 2009.
[32] J. Grabowski, M. de León, J. C. Marrero, and D. Martı́n de Diego. Nonholonomic constraints: a new viewpoint. J. Math. Phys., 50(1):013520, 17, 2009.
2
[33] Janusz Grabowski, Marek Kuś, and Giuseppe Marmo. Wigner’s theorem and the geometry
of extreme positive maps. J. Phys. A, 42(34):345301, 20, 2009.
[34] Janusz Grabowski and Mikolaj Rotkiewicz. Higher vector bundles and multi-graded symplectic manifolds. J. Geom. Phys., 59(9):1285–1305, 2009.
[35] Katarzyna Grabowska, Janusz Grabowski, and Pawel Urbański. The Schrödinger operator
as a generalized Laplacian. J. Phys. A, 41(14):145204, 20, 2008.
[36] Katarzyna Grabowska and Janusz Grabowski. Variational calculus with constraints on
general algebroids. J. Phys. A, 41(17):175204, 25, 2008.
[37] José F. Cariñena, Janusz Grabowski, and Giuseppe Marmo. Superposition rules, Lie
theorem, and partial differential equations. Rep. Math. Phys., 60(2):237–258, 2007.
[38] Katarzyna Grabowska, Janusz Grabowski, and Pawel Urbański. AV-differential geometry:
Euler-Lagrange equations. J. Geom. Phys., 57(10):1984–1998, 2007.
[39] J. Grabowski, D. Iglesias, J. C. Marrero, E. Padrón, and P. Urbański. Jacobi structures
on affine bundles. Acta Math. Sin. (Engl. Ser.), 23(5):769–788, 2007.
[40] Janusz Grabowski, Marek Kuś, and Giuseppe Marmo. On the relation between states and
maps in infinite dimensions. Open Syst. Inf. Dyn., 14(4):355–370, 2007.
[41] Janusz Grabowski. Local Lie algebra determines base manifold. In From geometry to quantum mechanics, volume 252 of Progr. Math., pages 131–145. Birkhäuser Boston, Boston,
MA, 2007.
[42] Janusz Grabowski and Norbert Poncin. On quantum and classical Poisson algebras. In
Geometry and topology of manifolds, volume 76 of Banach Center Publ., pages 313–324.
Polish Acad. Sci., Warsaw, 2007.
[43] Katarzyna Grabowska, Pawel Urbański, and Janusz Grabowski. Geometrical mechanics
on algebroids. Int. J. Geom. Methods Mod. Phys., 3(3):559–575, 2006.
[44] Janusz Grabowski. Courant-Nijenhuis tensors and generalized geometries. In Groups,
geometry and physics, Monogr. Real Acad. Ci. Exact. Fı́s.-Quı́m. Nat. Zaragoza, 29, pages
101–112. Acad. Cienc. Exact. Fı́s. Quı́m. Nat. Zaragoza, Zaragoza, 2006.
[45] Janusz Grabowski, Marek Kuś, and Giuseppe Marmo. Symmetries, group actions, and
entanglement. Open Syst. Inf. Dyn., 13(4):343–362, 2006.
[46] Janusz Grabowski, Giuseppe Marmo, and Peter W. Michor. Homology and modular classes
of Lie algebroids. Ann. Inst. Fourier (Grenoble), 56(1):69–83, 2006.
[47] Katarzyna Grabowska, Janusz Grabowski, and Pawel Urbański. Frame-independent mechanics: geometry on affine bundles. In Travaux mathématiques. Fasc. XVI, Trav. Math.,
XVI, pages 107–120. Univ. Luxemb., Luxembourg, 2005.
[48] J. Grabowski. Isomorphisms of algebras of smooth functions revisited. Arch. Math. (Basel),
85(2):190–196, 2005.
[49] J. Grabowski and N. Poncin. Derivations of the Lie algebras of differential operators.
Indag. Math. (N.S.), 16(2):181–200, 2005.
[50] Janusz Grabowski, Marek Kuś, and Giuseppe Marmo. Geometry of quantum systems:
density states and entanglement. J. Phys. A, 38(47):10217–10244, 2005.
3
[51] José F. Cariñena, Janusz Grabowski, and Giuseppe Marmo. Courant algebroid and Lie
bialgebroid contractions. J. Phys. A, 37(19):5189–5202, 2004.
[52] Katarzyna Grabowska, Janusz Grabowski, and Pawel Urbański. AV-differential geometry:
Poisson and Jacobi structures. J. Geom. Phys., 52(4):398–446, 2004.
[53] J. Grabowski, D. Iglesias, J. C. Marrero, E. Padrón, and P. Urbanski. Poisson-Jacobi
reduction of homogeneous tensors. J. Phys. A, 37(20):5383–5399, 2004.
[54] J. Grabowski and N. Poncin. Automorphisms of quantum and classical Poisson algebras.
Compos. Math., 140(2):511–527, 2004.
[55] Janusz Grabowski and Norbert Poncin. Lie algebraic characterization of manifolds. Cent.
Eur. J. Math., 2(5):811–825 (electronic), 2004.
[56] Janusz Grabowski, Giuseppe Marmo, and Pawel Urbański, editors. Classical and quantum
integrability, volume 59 of Banach Center Publications. Polish Academy of Sciences Institute of Mathematics, Warsaw, 2003. Dedicated to Wlodzimierz Tulczyjew, Papers from
the workshop held in Warsaw, August 27–September 1, 2001.
[57] Katarzyna Grabowska, Janusz Grabowski, and Pawel Urbański. Lie brackets on affine
bundles. Ann. Global Anal. Geom., 24(2):101–130, 2003.
[58] Janusz Grabowski and Giuseppe Marmo. Binary operations in classical and quantum
mechanics. In Classical and quantum integrability (Warsaw, 2001), volume 59 of Banach
Center Publ., pages 163–172. Polish Acad. Sci., Warsaw, 2003.
[59] Janusz Grabowski and Giuseppe Marmo. The graded Jacobi algebras and (co)homology.
J. Phys. A, 36(1):161–181, 2003.
[60] Janusz Grabowski. Quasi-derivations and QD-algebroids. Rep. Math. Phys., 52(3):445–
451, 2003.
[61] Janusz Grabowski and Pawel Urbański. On characterization of Poisson and Jacobi structures. Cent. Eur. J. Math., 1(1):123–140 (electronic), 2003.
[62] Mark J. Gotay, Janusz Grabowski, and Bryon Kaneshige. Polynomial algebras on coadjoint
orbits of semisimple Lie groups. J. Pure Appl. Algebra, 170(1):29–34, 2002.
[63] José F. Cariñena, Janusz Grabowski, and Giuseppe Marmo. Contractions: Nijenhuis and
Saletan tensors for general algebraic structures. J. Phys. A, 34(18):3769–3789, 2001.
[64] José F. Cariñena, Janusz Grabowski, and Giuseppe Marmo. Some physical applications
of systems of differential equations admitting a superposition rule. In Proceedings of the
XXXII Symposium on Mathematical Physics (Toruń, 2000), volume 48, pages 47–58, 2001.
[65] José F. Cariñena, Janusz Grabowski, and Arturo Ramos. Reduction of time-dependent
systems admitting a superposition principle. Acta Appl. Math., 66(1):67–87, 2001.
[66] Mark J. Gotay and Janusz Grabowski. On quantizing nilpotent and solvable basic algebras.
Canad. Math. Bull., 44(2):140–149, 2001.
[67] Janusz Grabowski and Katarzyna Grabowska. The Lie algebra of a Lie algebroid. In
Lie algebroids and related topics in differential geometry (Warsaw, 2000), volume 54 of
Banach Center Publ., pages 43–50. Polish Acad. Sci., Warsaw, 2001.
4
[68] Janusz Grabowski and Giuseppe Marmo.
34(49):10975–10990, 2001.
Jacobi structures revisited.
J. Phys. A,
[69] Janusz Grabowski and Giuseppe Marmo. Non-antisymmetric versions of Nambu-Poisson
and algebroid brackets. J. Phys. A, 34(18):3803–3809, 2001.
[70] Janusz Grabowski and Pawel Urbański, editors. Poisson geometry, volume 51 of Banach
Center Publications. Polish Academy of Sciences Institute of Mathematics, Warsaw, 2000.
Stanislaw Zakrzewski in memoriam, Papers from the workshop held in Warsaw, August
3–15, 1998.
[71] J. F. Cariñena, J. Grabowski, and G. Marmo. Lie-Scheffers systems: a geometric approach.
Napoli Series on Physics and Astrophysics. Bibliopolis, Naples, 2000.
[72] José F. Cariñena, Janusz Grabowski, and Giuseppe Marmo. Quantum bi-Hamiltonian
systems. Internat. J. Modern Phys. A, 15(30):4797–4810, 2000.
[73] Mark J. Gotay, Janusz Grabowski, and Hendrik B. Grundling. An obstruction to quantizing compact symplectic manifolds. Proc. Amer. Math. Soc., 128(1):237–243, 2000.
[74] J. Grabowski and G. Marmo. On Filippov algebroids and multiplicative Nambu-Poisson
structures. Differential Geom. Appl., 12(1):35–50, 2000.
[75] Janusz Grabowski. Isomorphisms of Poisson and Jacobi brackets. In Poisson geometry (Warsaw, 1998), volume 51 of Banach Center Publ., pages 79–85. Polish Acad. Sci.,
Warsaw, 2000.
[76] Antonio Campillo, Janusz Grabowski, and Gerd Müller. Derivation algebras of toric varieties. Compositio Math., 116(2):119–132, 1999.
[77] J. Grabowski, G. Marmo, and P. W. Michor. Construction of completely integrable systems
by Poisson mappings. Modern Phys. Lett. A, 14(30):2109–2118, 1999.
[78] J. Grabowski and G. Marmo. Remarks on Nambu-Poisson and Nambu-Jacobi brackets.
J. Phys. A, 32(23):4239–4247, 1999.
[79] J. Grabowski and P. Urbański. Algebroids—general differential calculi on vector bundles.
J. Geom. Phys., 31(2-3):111–141, 1999.
[80] Janusz Grabowski. Homotopically non-trivial additive subgroups of Hilbert spaces. Proc.
Amer. Math. Soc., 127(5):1563–1565, 1999.
[81] D. Alekseevsky, J. Grabowski, G. Marmo, and P. W. Michor. Poisson structures on double
Lie groups. J. Geom. Phys., 26(3-4):340–379, 1998.
[82] J. Grabowski and G. Marmo. Generalized n-Poisson brackets on a symplectic manifold.
Modern Phys. Lett. A, 13(39):3185–3192, 1998.
[83] Janusz Grabowski. Poisson Lie groups in infinite dimensions. In Analysis on infinitedimensional Lie groups and algebras (Marseille, 1997), pages 94–103. World Sci. Publ.,
River Edge, NJ, 1998.
[84] D. V. Alekseevsky, J. Grabowski, G. Marmo, and P. W. Michor. Completely integrable
systems—a generalization. Modern Phys. Lett. A, 12(22):1637–1648, 1997.
[85] J. Grabowski and P. Urbański. Tangent and cotangent lifts and graded Lie algebras
associated with Lie algebroids. Ann. Global Anal. Geom., 15(5):447–486, 1997.
5
[86] Janusz Grabowski. Z-graded extensions of Poisson brackets. Rev. Math. Phys., 9(1):1–27,
1997.
[87] Janusz Grabowski and Pawel Urbański. Lie algebroids and Poisson-Nijenhuis structures.
Rep. Math. Phys., 40(2):195–208, 1997. Quantizations, deformations and coherent states
(Bialowieża, 1996).
[88] Tadeusz Dobrowolski, Janusz Grabowski, and Kazuhiro Kawamura. Topological type of
weakly closed subgroups in Banach spaces. Studia Math., 118(1):49–62, 1996.
[89] J. Grabowski and G. Marmo. Deformed Tulczyjew triples and Legendre transform. Rend.
Sem. Mat. Univ. Politec. Torino, 54(3):279–294, 1996. Geometrical structures for physical
theories, I (Vietri, 1996).
[90] J. Grabowski, G. Marmo, A. Perelomov, and A. Simoni. Remarks on Virasoro and KacMoody algebras. Internat. J. Modern Phys. A, 11(28):4969–4984, 1996.
[91] J. Grabowski. Gelfand-Fuks-Virasoro cocycle and a Poisson Lie structure on Diff[0, 2π].
In Quantum groups (Karpacz, 1994), pages 587–598. PWN, Warsaw, 1995.
[92] J. Grabowski and P. Urbański. Tangent lifts of Poisson and related structures. J. Phys.
A, 28(23):6743–6777, 1995.
[93] Janusz Grabowski. Deformational quantization of Poisson structures. Rep. Math. Phys.,
35(2-3):267–281, 1995. Mathematics as language and art (Bialowieża, 1993).
[94] Janusz Grabowski. Poisson Lie groups and their relations to quantum groups. In Panoramas of mathematics (Warsaw, 1992/1994), volume 34 of Banach Center Publ., pages
55–64. Polish Acad. Sci., Warsaw, 1995.
[95] D. Alekseevsky, J. Grabowski, G. Marmo, and P. W. Michor. Poisson structures on the
cotangent bundle of a Lie group or a principal bundle and their reductions. J. Math. Phys.,
35(9):4909–4927, 1994.
[96] Fredric D. Ancel, Tadeusz Dobrowolski, and Janusz Grabowski. Closed subgroups in
Banach spaces. Studia Math., 109(3):277–290, 1994.
[97] J. Grabowski, G. Landi, G. Marmo, and G. Vilasi. Generalized reduction procedure:
symplectic and Poisson formalism. Fortschr. Phys., 42(5):393–427, 1994.
[98] Janusz Grabowski. Hochschild cohomology and quantization of Poisson structures. Rend.
Circ. Mat. Palermo (2) Suppl., (37):87–91, 1994. Geometry and physics (Zdı́kov, 1993).
[99] Janusz Grabowski. A Poisson-Lie structure on the diffeomorphism group of a circle. Lett.
Math. Phys., 32(4):307–313, 1994.
[100] J. Grabowski, G. Marmo, and A. M. Perelomov. Poisson structures: towards a classification. Modern Phys. Lett. A, 8(18):1719–1733, 1993.
[101] Janusz Grabowski. Derivative of the exponential mapping for infinite-dimensional Lie
groups. Ann. Global Anal. Geom., 11(3):213–220, 1993.
[102] Janusz Grabowski. Ideals of the Lie algebras of vector fields. In The Proceedings of the
Winter School Geometry and Topology (Srnı́, 1992), number 32, pages 89–95, 1993.
[103] Janusz Grabowski. Lie algebras of vector fields and generalized foliations. Publ. Mat.,
37(2):359–367, 1993.
6
[104] Janusz Grabowski. Universal enveloping algebras and quantization. In Proceedings of the
Winter School “Geometry and Physics” (Srnı́, 1991), number 30, pages 66–70, 1993.
[105] Tadeusz Dobrowolski and Janusz Grabowski. Subgroups of Hilbert spaces. Math. Z.,
211(4):657–669, 1992.
[106] J. Grabowski. Abstract Jacobi and Poisson structures. Quantization and star-products.
J. Geom. Phys., 9(1):45–73, 1992.
[107] J. Grabowski. Abstract Poisson structures and star-products. In Differential geometry
and its applications (Eger, 1989), volume 56 of Colloq. Math. Soc. János Bolyai, pages
387–394. North-Holland, Amsterdam, 1992.
[108] C. J. Atkin and J. Grabowski. Homomorphisms of the Lie algebras associated with a
symplectic manifold. Compositio Math., 76(3):315–349, 1990.
[109] Janusz Grabowski. Quantum SU(2) group of Woronowicz and Poisson structures. In
Differential geometry and its applications (Brno, 1989), pages 313–322. World Sci. Publ.,
Teaneck, NJ, 1990.
[110] Janusz Grabowski. Remarks on nilpotent Lie algebras of vector fields. J. Reine Angew.
Math., 406:1–4, 1990.
[111] Janusz Grabowski and Wojciech Wojtyński. Quotient groups of linear topological spaces.
Colloq. Math., 59(1):35–51, 1990.
[112] Janusz Grabowski. General Poisson algebras. In Proceedings of the Winter School on
Geometry and Physics (Srnı́, 1988), number 21, pages 217–222, 1989.
[113] Janusz Grabowski. Free subgroups of diffeomorphism groups. Fund. Math., 131(2):103–
121, 1988.
[114] Janusz Grabowski. Derivations of the Lie algebras associated with a symplectic structure.
In Differential geometry and its applications, communications (Brno, 1986), pages 117–
125. Univ. J. E. Purkyně, Brno, 1987.
[115] Janusz Grabowski. Lie algebras connected with associative ones. In Proceedings of the
13th winter school on abstract analysis (Srnı́, 1985), number 9, pages 109–116 (1986),
1985.
[116] Janusz Grabowski. The Lie structure of C ∗ and Poisson algebras. Studia Math., 81(3):259–
270, 1985.
[117] W. Banaszczyk and J. Grabowski. Connected subgroups of nuclear spaces. Studia Math.,
78(2):161–163, 1984.
[118] Janusz Grabowski. Groups of diffeomorphisms and Lie theory. In Proceedings of the 11th
winter school on abstract analysis (Železná Ruda, 1983), number Suppl. 3, pages 141–147,
1984.
[119] Janusz Grabowski. Derivations of the Lie algebras of analytic vector fields. Compositio
Math., 43(2):239–252, 1981.
[120] J. Grabowski. Isomorphisms and ideals of the Lie algebras of vector fields. Invent. Math.,
50, 1978.
7
[121] Janusz Grabowski. On the structure of ideals and isomorphisms of some Lie algebras
of vectorfields. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 26(5):425–427,
1978.
8