On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures

Josef Janyška

Archivum Mathematicum (2016)

  • Volume: 052, Issue: 5, page 325-339
  • ISSN: 0044-8753

Abstract

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We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by pairs generating infinitesimal symmetries of basic tensor fields given by the almost-cosymplectic-contact structure.

How to cite

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Janyška, Josef. "On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures." Archivum Mathematicum 052.5 (2016): 325-339. <http://eudml.org/doc/287577>.

@article{Janyška2016,
abstract = {We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by pairs generating infinitesimal symmetries of basic tensor fields given by the almost-cosymplectic-contact structure.},
author = {Janyška, Josef},
journal = {Archivum Mathematicum},
keywords = {almost-cosymplectic-contact structure; almost-coPoisson-Jacobi structure; infinitesimal symmetry; Lie algebra},
language = {eng},
number = {5},
pages = {325-339},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures},
url = {http://eudml.org/doc/287577},
volume = {052},
year = {2016},
}

TY - JOUR
AU - Janyška, Josef
TI - On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures
JO - Archivum Mathematicum
PY - 2016
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 052
IS - 5
SP - 325
EP - 339
AB - We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by pairs generating infinitesimal symmetries of basic tensor fields given by the almost-cosymplectic-contact structure.
LA - eng
KW - almost-cosymplectic-contact structure; almost-coPoisson-Jacobi structure; infinitesimal symmetry; Lie algebra
UR - http://eudml.org/doc/287577
ER -

References

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  5. Janyška, J., Modugno, M., 10.1016/j.matpur.2008.09.007, J. Math. Pures Appl. (9) 91 (2009), 211–232. (2009) Zbl1163.53051MR2498755DOI10.1016/j.matpur.2008.09.007
  6. Janyška, J., Vitolo, R., 10.1088/1751-8113/45/48/485205, J. Phys. A: Math. Theor. 45 (2012), 485205. (2012) Zbl1339.70036MR2998421DOI10.1088/1751-8113/45/48/485205
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  8. Kolář, I., Michor, P.W., Slovák, J., Natural Operations in Differential Geometry, Springer, 1993. (1993) MR1202431
  9. Lichnerowicz, A., Les variétés de Jacobi et leurs algèbres de Lie associées, J. Math. Pures Appl. (9) 57 (1978), 453–488. (1978) Zbl0407.53025MR0524629
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  11. Vaisman, I., Lectures on the Geometry of Poisson Manifolds, Birkhäuser Verlag, Basel–Boston–Berlin, 1994. (1994) Zbl0810.53019MR1269545

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