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Quasi-Poisson Manifolds

Published online by Cambridge University Press:  20 November 2018

A. Alekseev ,
Y. Kosmann-Schwarzbach  and
E. Meinrenken
A. Alekseev
Affiliation:
Institute for Theoretical Physics Uppsala University Box 803 S-75108 Uppsala Sweden, email: [email protected]
Y. Kosmann-Schwarzbach
Affiliation:
Centre de Mathématiques (U.M.R. du C.N.R.S. 7640) Ecole Polytechnique F-91128 Palaiseau France, email: [email protected]
E. Meinrenken
Affiliation:
University of Toronto Department of Mathematics 100 St George Street Toronto, Ontario M5S3G3, email: [email protected]
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Abstract

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A quasi-Poisson manifold is a $G$-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in ${{\Lambda }^{3}}\mathfrak{g}$ associated to an invariant inner product. We introduce the concept of the fusion of such manifolds, and we relate the quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.

Keywords

53D
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 1 , 01 February 2002 , pp. 3 - 29
Copyright
Copyright © Canadian Mathematical Society 2002

References

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