2015/04/30 by María Julia Redondo, Maria Julia Redondo, Lucrecia Román +1
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Computer science #Cup product #De Rham cohomology #Equivariant cohomology #Homotopy and Cohomology in Algebraic Topology #Mathematics #Morphism #Pure mathematics #Quiver #Resolution (logic) #String (physics) #math.RA #msc:16E40 #msc:16W99
paper · pdf · doi:10.1007/s10468-017-9704-1
Final version to appear in Algebras and Representation Theory, 33 pages
arxiv created 2017/05/24 · arxiv updated 2017/05/25 · openalex publication_date 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe the Gerstenhaber algebra structure on the Hochschild cohomology HH*(A) when A is a quadratic string algebra. First we compute the Hochschild cohomology groups using Barzdell's resolution and we describe generators of these groups. Then we construct comparison morphisms between the bar resolution and Bardzell's resolution in order to get formulae for the cup product and the Lie bracket. We find conditions on the bound quiver associated to string algebras in order to get non-trivial structures.