2011/07/05 by Graciela Carboni, Jorge A. Guccione, Carboni, Graciela +5
Mathematics · #16E40 #16T05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:16E40 #msc:16T05
paper · pdf · doi:10.48550/arxiv.1107.0951
63 pages
arxiv created 2011/07/05 · openalex publication_date 2011/07/05 · arxiv updated 2011/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1V. We obtain a mixed complex, simpler that the canonical one, that gives the Hochschild, cyclic, negative and periodic homology of a crossed product E:=A#f V, in the sense of Brzezinski. We actually work in the more general context of relative cyclic homology. Specifically, we consider a subalgebra K of A that satisfies suitable hypothesis and we find a mixed complex computing the Hochschild, cyclic, negative and periodic homology of E relative to K. Then, when E is a cleft braided Hopf crossed product, we obtain a simpler mixed complex, that also gives the Hochschild, cyclic, negative and periodic homology of E.