The Bv Algebra on Hochschild Cohomology Induced by Infinity Inner Products

A Proof of a Cyclic Version of Deligne’s Conjecture via Cacti

We generalize our results on Deligne’s conjecture to prove the statement that the normalized Hochschild co–chains of a finite–dimensional associative algebra with a non–degenerate, symmetric, invariant inner product are an algebra over a chain model of the framed little discs operad which is given by cacti. In particular, in characteristic zero they are a BV algebra up to homotopy and the Hochs...

On the Cyclic Deligne Conjecture

Let A be a finite dimensional, unital, and associative algebra which is endowed with a non-degenerate and invariant inner product. We give an explicit description of an action of cyclic Sullivan chord diagrams on the normalized Hochschild cochain complex of A. As a corollary, the Hochschild cohomology of A becomes a Frobenius algebra which is endowed with a compatible BV operator. If A is also ...

Second Hochschild Cohomology of Convolution Algebras

On the Hochschild homology of open Frobenius algebras

We prove that the Hochschild homology (and cohomology) of a symmetric open Frobenius algebra A has a natural coBV and BV structure. The underlying coalgebra and algebra structure may not be resp. counital and unital. Moreover we prove that the product and coproduct satisfy the Frobenius compatibility condition i.e. the coproduct on HH∗(A) is a map of left and right HH∗(A)-modules. If A is commu...

On algebraic structures of the Hochschild complex

We first review various known algebraic structures on the Hochschild (co)homology of a differential graded algebras under weak Poincaré duality hypothesis, such as CalabiYau algebras, derived Poincaré duality algebras and closed Frobenius algebras. This includes a BV-algebra structure on HH(A,A) or HH(A,A), which in the latter case is an extension of the natural Gerstenhaber structure on HH(A,A...