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Integration of Lie algebroid comorphisms


Cattaneo, Alberto S; Dherin, Benoît; Weinstein, Alan (2013). Integration of Lie algebroid comorphisms. Portugaliae mathematica, 70(2):113-144.

Abstract

We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the of integrable Lie algebroids and complete Lie algebroid comorphisms to the of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplectization functor in Poisson geometry. We include examples to show that the integrability of comorphisms and Poisson maps may not hold in the absence of a completeness assumption.

Abstract

We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the of integrable Lie algebroids and complete Lie algebroid comorphisms to the of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplectization functor in Poisson geometry. We include examples to show that the integrability of comorphisms and Poisson maps may not hold in the absence of a completeness assumption.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2013
Deposited On:22 Nov 2013 11:50
Last Modified:05 Apr 2016 17:10
Publisher: European Mathematical Society Publishing House
ISSN: 0032-5155
Publisher DOI:https://doi.org/10.4171/PM/1928

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