2007/07/21 by Mariano Suárez-Álvarez, Suárez-Alvarez, Mariano · 2 citations
Mathematics · #13D03. #18G15 #18G40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.0707.3210
openalex publication_date 2007/07/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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.