2001/07/27 by Jorge A. Guccione, Guccione, Jorge A., Juan J. Guccione +1
Mathematics · #16C40 #16D20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:16C40 #msc:16D20
paper · pdf · doi:10.48550/arxiv.math/0107200
17 pages. This is a enterely rewriten version of the paper entitled "Cohomology of split algebras". We have made substancial changes in the third section of the previous version
openalex publication_date 2001/07/27 · arxiv created 2001/08/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain a decomposition for the Hochschild cochain complex of a split algebra and we study some properties of the cohomology of each term of this decomposition. Then, we consider the case of trivial extensions, specially of Frobenius algebras. In particular, we determine completely the cohomology of the trivial extension of a finite dimensional Hopf algebra. Finally, as an application, we obtain a result about the Hochschild cohomology of Frobenius algebras.