Automorphismes, graduations et categories triangulees

Details Automorphismes, graduations et categories triangulees Automorphismes, graduations et categories triangulees

2010-08-11

arxiv.org/abs/1008.1971v1

Mathematics

Representation Theory

Scientific paper

We give a moduli interpretation of the outer automorphism group Out of a finite dimensional algebra similar to that of the Picard group of a scheme. We deduce that Out^0 is invariant under derived and stable equivalences. This allows us to transfer gradings between algebras and gives rise to conjectural homological constructions of interesting gradings on block of finite groups with abelian defect. We give applications to the lifting of stable equivalences to derived equivalences. We give a counterpart of the invariance result for smooth projective varieties: the product Pic^0xAut^0 is invariant under derived equivalence.

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