The H-Covariant Strong Picard Groupoid

Details The H-Covariant Strong Picard Groupoid The H-Covariant Strong Picard Groupoid

2004-09-08

arxiv.org/abs/math/0409130v2

Mathematics

Quantum Algebra

LaTeX 2e, 50 pages. Revised version with additional examples and references. To appear in JPAA

Scientific paper

The notion of H-covariant strong Morita equivalence is introduced for *-algebras over C = R(i) with an ordered ring R which are equipped with a *-action of a Hopf *-algebra H. This defines a corresponding H-covariant strong Picard groupoid which encodes the entire Morita theory. Dropping the positivity conditions one obtains H-covariant *-Morita equivalence with its H-covariant *-Picard groupoid. We discuss various groupoid morphisms between the corresponding notions of the Picard groupoids. Moreover, we realize several Morita invariants in this context as arising from actions of the H-covariant strong Picard groupoid. Crossed products and their Morita theory are investigated using a groupoid morphism from the H-covariant strong Picard groupoid into the strong Picard groupoid of the crossed products.

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