2023/11/28 by Mikhailo Dokuchaev, Dokuchaev, Mikhailo, Emmanuel Jerez +1 · 2 citations
Mathematics · #16E40 #18G40 #20C25 #20J05 #20J06 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 16S35 #Rings and Algebras (math.RA) #Secondary 16E30
paper · pdf · doi:10.48550/arxiv.2311.16999
openalex publication_date 2023/11/28 · openalex created_date 2023/11/30 · openalex updated_date 2026/07/28
Given a group G and a partial factor set σ of G, we introduce the twisted partial group algebra κparσG, which governs the partial projective σ-representations of G into algebras over a filed κ. Using the relation between partial projective representations and twisted partial actions we endow κparσG with the structure of a crossed product by a twisted partial action of G on a commutative subalgebra of κparσ G. Then, we use twisted partial group algebras to obtain a first quadrant Grothendieck spectral sequence converging to the Hochschild homology of the crossed product A∗Θ G, involving the Hochschild homology of A and the partial homology of G, where Θ is a unital twisted partial action of G on a κ-algebra A with a κ-based twist. An analogous third quadrant cohomological spectral sequence is also obtained.