Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds

Details Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds

2010-04-06

arxiv.org/abs/1004.0875v2

Mathematics

Quantum Algebra

28 pages. Minor update, fixed typos.

Scientific paper

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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