2012/09/30 by Van C. Nguyen · 11 citations
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Chemistry #Cohomology #Cohomology ring #Equivariant cohomology #Field (mathematics) #Finite Group Theory Research #Group cohomology #Hopf algebra #Mathematics #Pure mathematics #Ring (chemistry) #math.KT #math.RA #math.RT
paper · pdf · doi:10.1016/j.jpaa.2013.01.008
published in Journal of Pure and Applied Algebra 217(10), 1967-1979 (Elsevier BV) · 18 pages, simplified from the first version, to appear in J. Pure and Applied Algebra
arxiv created 2013/01/08 · openalex publication_date 2013/03/07 · arxiv updated 2013/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let A be any finite dimensional Hopf algebra over a field k. We specify the Tate and Tate-Hochschild cohomology for A and introduce cup products that make them become graded rings. We establish the relationship between these rings. In particular, the Tate-Hochschild cohomology of A is isomorphic (as algebras) to its Tate cohomology with coefficients in an adjoint module. Consequently, the Tate cohomology ring of A is a direct summand of its Tate-Hochschild cohomology ring. As an example, we explicitly compute both the Tate and Tate-Hochschild cohomology for the Sweedler algebra H4.