2018/03/28 by Joanna Meinel, Meinel, Joanna, Van C. Nguyen +7
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1803.10909
We determine the Gerstenhaber structure on the Hochschild cohomology ring of\na class of self-injective special biserial algebras. Each of these algebras is\npresented as a quotient of the path algebra of a certain quiver. In degree one,\nwe show that the cohomology is isomorphic, as a Lie algebra, to a direct sum of\ncopies of a subquotient of the Virasoro algebra. These copies share Virasoro\ndegree 0 and commute otherwise. Finally, we describe the cohomology in degree\nn as a module over this Lie algebra by providing its decomposition as a\ndirect sum of indecomposable modules.\n