KFU. Card publication. Lifts of Poisson structures to Weil bundle

LIFTS OF POISSON STRUCTURES TO WEIL BUNDLE

Form of presentation

Articles in Russian journals and collections

Year of publication

2012

Язык

английский

Authors, employees of KFU

Shurygin Vadim Vadimovich, author

Bibliographic description in the original language

Lifts of Poisson structures to Weil bundle. Lobachevskii J. Math., 2012, Vol. 33, No. 1, pp. 75-107.

Annotation

Lobachevskii Journal of Mathematics

Keywords

Poisson structure, modular class, Weil algebra, Weil bundle, Frobenius algebra, complete lift, vertical lift.

The name of the journal

Lobachevskii Journal of Mathematics

Please use this ID to quote from or refer to the card

Field DC	Value	Language
dc.contributor.author	Shurygin Vadim Vadimovich	ru_RU
dc.date.accessioned	2012-01-01T00:00:00Z	ru_RU
dc.date.available	2012-01-01T00:00:00Z	ru_RU
dc.date.issued	2012	ru_RU
dc.identifier.citation	Lifts of Poisson structures to Weil bundle. Lobachevskii J. Math., 2012, Vol. 33, No. 1, pp. 75-107.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=40162&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	In the present paper, we study complete and vertical lifts of tensor ﬁelds from a smooth manifold M to its Weil bundle T^AM deﬁned by a Frobenius Weil algebra A. For a Poisson manifold (M,w), we show that the complete lift w^C and the vertical lift w^V of the Poisson tensor w are Poisson tensors on T^AM and establish their properties. We prove that the complete and the vertical lifts induce homomorphisms of the Poisson cohomology spaces. We compute the modular classes of the lifts of Poisson structures.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Poisson structure	ru_RU
dc.subject	modular class	ru_RU
dc.subject	Weil algebra	ru_RU
dc.subject	Weil bundle	ru_RU
dc.subject	Frobenius algebra	ru_RU
dc.subject	complete lift	ru_RU
dc.subject	vertical lift.	ru_RU
dc.title	Lifts of Poisson structures to Weil bundle	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU