On the Hochschild homology of open Frobenius algebras

  • Hossein Abbaspour

    Université de Nantes, France

Abstract

We prove that the shifted Hochschild homology of a symmetric open Frobenius algebra of degree has a natural coBV-algebra structure which is defined at the chain level. As a consequence is a BV algebra. The underlying coalgebra and algebra structure may not be resp. counital and unital. We also introduce a natural BV-algebra structure on which is also defined at the chain level. Hence there is a BV-structure on . Moreover we prove that the product and coproduct on~ satisfy the Frobenius compatibility condition i.e. is an open Frobenius algebras. If is commutative, we also introduce a natural BV structure on the shifted relative Hochschild homology . We conjecture that the product of this BV structure is identical to the Goresky–Hingston [10] product on the cohomology of free loop spaces when is a commutative cochain algebra model for .

Cite this article

Hossein Abbaspour, On the Hochschild homology of open Frobenius algebras. J. Noncommut. Geom. 10 (2016), no. 2, pp. 709–743

DOI 10.4171/JNCG/246