# Isomorphisms of Poisson and Jacobi brackets

Banach Center Publications (2000)

- Volume: 51, Issue: 1, page 79-85
- ISSN: 0137-6934

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topGrabowski, Janusz. "Isomorphisms of Poisson and Jacobi brackets." Banach Center Publications 51.1 (2000): 79-85. <http://eudml.org/doc/209046>.

@article{Grabowski2000,

abstract = {We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as, for example, those given by Poisson or contact structures. We admit degenerate structures as well, which seems to be new in the literature.},

author = {Grabowski, Janusz},

journal = {Banach Center Publications},

keywords = {isomorphisms; local Lie algebra; Poisson; contact},

language = {eng},

number = {1},

pages = {79-85},

title = {Isomorphisms of Poisson and Jacobi brackets},

url = {http://eudml.org/doc/209046},

volume = {51},

year = {2000},

}

TY - JOUR

AU - Grabowski, Janusz

TI - Isomorphisms of Poisson and Jacobi brackets

JO - Banach Center Publications

PY - 2000

VL - 51

IS - 1

SP - 79

EP - 85

AB - We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as, for example, those given by Poisson or contact structures. We admit degenerate structures as well, which seems to be new in the literature.

LA - eng

KW - isomorphisms; local Lie algebra; Poisson; contact

UR - http://eudml.org/doc/209046

ER -

## References

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- [5] F. Guedira and A. Lichnerowicz, Géométrie des algèbres de Lie locales de Kirillov, J. Math. pures et appl. 63 (1984), 407-484. Zbl0562.53029
- [6] A. A. Kirillov, Local Lie algebras, Russ. Math. Surv. 31 (1976), 55-75. Zbl0357.58003
- [7] A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Differential Geom. 12 (1977), 253-300. Zbl0405.53024
- [8] A. Lichnerowicz, Les variétés de Jacobi et leurs algèbres de Lie associées, J. Math. pures et appl. 57 (1978), 453-488. Zbl0407.53025
- [9] H. Omori, Infinite Dimensional Lie Transformation Groups, Lecture Notes in Math. 427, Springer, Berlin, 1974. Zbl0328.58005
- [10] S. M. Skriabin, Lie algebras of derivations of commutative rings: Generalizations of the Lie algebras of Cartan type, Preprint WINITI 4405-W87, Moscow University, 1987 (in Russian).
- [11] A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geom. 18 (1983), 523-557. Zbl0524.58011

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