Letters in Mathematical Physics vol:100 issue:2 pages:203-236
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.