Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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dc.contributor.author	Kosmann-Schwarzbach, Y.
dc.date.accessioned	2019-02-19T12:53:16Z
dc.date.available	2019-02-19T12:53:16Z
dc.date.issued	2008
dc.identifier.citation	Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey / Y. Kosmann-Schwarzbach // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 127 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2000 Mathematics Subject Classification: 17B70; 17B56; 17B66; 53C15; 58A10; 15A66; 17B81; 17-02; 53-02; 58-02
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149002
dc.description.abstract	After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. I express my sincere gratitude to the organizers of the Midwest Geometry Conference in memory of Thomas Branson which was held at the University of Iowa in May 2007. Thomas Branson and I collaborated on an article in the early 80’s, and the conference was a much appreciated opportunity to honor his memory and to learn about the considerable development of the topic in which we were both interested at the time, conformal invariance. The present article incorporates many results due to Camille Laurent-Gengoux, Franco Magri, Alan Weinstein and Milen Yakimov, which have appeared in our joint publications and preprints. I would like to extend my sincere thanks to them for all they taught me, and I thank Camille, in particular, for his remarks on an early version of this paper. My thanks also to Tudor Ratiu for reminding me of the early history of the bracket of dif ferential forms. This survey takes into account most of the suggestions of the referees to whom I am most grateful for their very substantial and constructive comments.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA