Morita Contexts, Idempotents, and Hochschild Cohomology - with Applications to Invariant Rings -

Details Morita Contexts, Idempotents, and Hochschild Cohomology - with Applications to Invariant Rings - Morita Contexts, Idempotents, and Hochschild Cohomology - with Applications to Invariant Rings -

2003-01-29

arxiv.org/abs/math/0301347v1

Mathematics

Commutative Algebra

28 pages, uses conm-p-l.sty. To appear in Contemporary Mathematics series volume (Conference Proceedings for Summer 2001 Greno

Scientific paper

We investigate how to compare Hochschild cohomology of algebras related by a Morita context. Interpreting a Morita context as a ring with distinguished idempotent, the key ingredient for such a comparison is shown to be the grade of the Morita defect, the quotient of the ring modulo the ideal generated by the idempotent. Along the way, we show that the grade of the stable endomorphism ring as a module over the endomorphism ring controls vanishing of higher groups of selfextensions, and explain the relation to various forms of the Generalized Nakayama Conjecture for Noetherian algebras. As applications of our approach we explore to what extent Hochschild cohomology of an invariant ring coincides with the invariants of the Hochschild cohomology.

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