Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds |
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| Authors: | Stefan Jansen Nikolai Neumaier Gregor Schaumann Stefan Waldmann |
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| Affiliation: | 1.Fakult?t für Mathematik und Physik,Albert-Ludwigs-Universit?t Freiburg, Physikalisches Institut,Freiburg,Germany;2.Department Mathematik,Friedrich-Alexander-Universit?t Erlangen-Nürnberg,Erlangen,Germany;3.Department of Mathematics,Katholieke Universiteit Leuven,Heverlee,Belgium |
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| Abstract: | In this paper we investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We consider three types of Morita theory: ring-theoretic equivalence, *-equivalence, and strong equivalence. Then we apply these general considerations to star product algebras over symplectic manifolds with a Lie algebra symmetry. We obtain the full classification up to equivariant Morita equivalence. |
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