Remarks on local Lie algebras of pairs of functions

Josef Janyška

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 3, page 687-709
  • ISSN: 0011-4642

Abstract

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Starting by the famous paper by Kirillov, local Lie algebras of functions over smooth manifolds were studied very intensively by mathematicians and physicists. In the present paper we study local Lie algebras of pairs of functions which generate infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds.

How to cite

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Janyška, Josef. "Remarks on local Lie algebras of pairs of functions." Czechoslovak Mathematical Journal 68.3 (2018): 687-709. <http://eudml.org/doc/294526>.

@article{Janyška2018,
abstract = {Starting by the famous paper by Kirillov, local Lie algebras of functions over smooth manifolds were studied very intensively by mathematicians and physicists. In the present paper we study local Lie algebras of pairs of functions which generate infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds.},
author = {Janyška, Josef},
journal = {Czechoslovak Mathematical Journal},
keywords = {almost-cosymplectic-contact structure; almost-coPoisson-Jacobi structure; infinitesimal symmetry; local Lie algebra},
language = {eng},
number = {3},
pages = {687-709},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on local Lie algebras of pairs of functions},
url = {http://eudml.org/doc/294526},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Janyška, Josef
TI - Remarks on local Lie algebras of pairs of functions
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 687
EP - 709
AB - Starting by the famous paper by Kirillov, local Lie algebras of functions over smooth manifolds were studied very intensively by mathematicians and physicists. In the present paper we study local Lie algebras of pairs of functions which generate infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds.
LA - eng
KW - almost-cosymplectic-contact structure; almost-coPoisson-Jacobi structure; infinitesimal symmetry; local Lie algebra
UR - http://eudml.org/doc/294526
ER -

References

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  1. León, M. de, Tuynman, G. M., 10.1016/0393-0440(96)00047-2, J. Geom. Phys. 20 (1996), 77-86. (1996) Zbl0861.53026MR1407405DOI10.1016/0393-0440(96)00047-2
  2. Janyška, J., 10.1063/1.4733369, AIP Conf. Proc. 1460, XX Internat. Fall Workshop on Geometry and Physics (2012), 135-140. (2012) DOI10.1063/1.4733369
  3. Janyška, J., 10.5817/AM2014-5-297, Arch. Math., Brno 50 (2014), 297-316. (2014) Zbl1340.70017MR3303779DOI10.5817/AM2014-5-297
  4. Janyška, J., 10.5817/AM2015-5-297, Arch. Math., Brno 51 (2015), 297-313. (2015) Zbl06537732MR3449110DOI10.5817/AM2015-5-297
  5. Janyška, J., 10.5817/AM2016-5-325, Arch. Math., Brno 52 (2016), 325-339. (2016) Zbl06674908MR3610867DOI10.5817/AM2016-5-325
  6. Janyška, J., Modugno, M., 10.1016/j.matpur.2005.11.004, J. Math. Pures Appl. (9) 85 (2006), 687-697. (2006) Zbl1113.53020MR2229665DOI10.1016/j.matpur.2005.11.004
  7. Janyška, J., Modugno, M., 10.1142/S021988780800303X, Int. J. Geom. Methods Mod. Phys. 5 (2008), 699-754. (2008) Zbl1116.53008MR2445392DOI10.1142/S021988780800303X
  8. 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
  9. Janyška, J., Vitolo, R., 10.1088/1751-8113/45/48/485205, J. Phys. A, Math. Theor. 45 (2012), Article ID 485205, 28 pages. (2012) Zbl1339.70036MR2998421DOI10.1088/1751-8113/45/48/485205
  10. Kirillov, A. A., 10.1070/RM1976v031n04ABEH001556, Russ. Math. Surv. 31 (1976), 55-75. (1976) Zbl0357.58003MR0438390DOI10.1070/RM1976v031n04ABEH001556
  11. Lichnerowicz, A., Les variétés de Jacobi et leurs algèbres de Lie associées, J. Math. Pures Appl., IX. Sér. 57 (1978), 453-488 French. (1978) Zbl0407.53025MR0524629
  12. Mackenzie, K. C. H., 10.1017/CBO9781107325883, London Mathematical Society, Lecture Note Series 213, Cambridge University Press, Cambridge (2005). (2005) Zbl1078.58011MR2157566DOI10.1017/CBO9781107325883
  13. Olver, P. J., 10.1007/978-1-4684-0274-2, Graduate Texts in Mathematics 107, Springer, New York (1986). (1986) Zbl0588.22001MR0836734DOI10.1007/978-1-4684-0274-2
  14. Shiga, K., 10.2969/jmsj/02620324, J. Math. Soc. Japan 26 (1974), 324-361. (1974) Zbl0273.58002MR0368025DOI10.2969/jmsj/02620324
  15. Sommers, P., 10.1063/1.1666395, J. Mathematical Phys. 14 (1973), 787-790. (1973) MR0329558DOI10.1063/1.1666395
  16. Vaisman, I., 10.1007/978-3-0348-8495-2, Progress in Mathematics 118, Birkhäuser, Basel (1994). (1994) Zbl0810.53019MR1269545DOI10.1007/978-3-0348-8495-2

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