Applications of the change of ring spectral sequence to the computation of Hochschild cohomology

MARIANO SUÁREZ-ALVAREZ

Mar del Plata

Congreso; Métodos homológicos y representaciones de Álgebras no conmutativas; 2006

Centre International de Mathématiques Pures et Appliquées

We consider the change-of-rings spectral sequence as it applies to Hochschild cohomology, obtaining a description of the differentials on the first page which relates it to the multiplicative stucture on cohomology. Using this information, we are able to completely describe the cohomology structure of monogenic algebras as well as some information on the structure of the cohomology in more general situations. We also show how to use the spectral sequence to reprove and generalize results of M. Auslander et al. about homological epimorphisms. We derive from this a rather general version of the long exact sequence due to D. Happel for a one-point (co)-extension of a finite dimensional algebra and show how it can be put to use in concrete examples.