The Hochschild Cohomology of a Poincaré Algebra
نویسنده
چکیده
In this note, we define the notion of a cactus set, and show that its geometric realization has a natural structure as an algebra over Voronov’s cactus operad, which is equivalent to the framed 2-dimensional little disks operad D2. Using this, we show that for a Poincaré algebra A, its Hochschild cohomology is an algebra over the (chain complexes of) D2.
منابع مشابه
Poincaré Duality at the Chain Level, and a Bv Structure on the Homology of the Free Loops Space of a Simply Connected Poincaré Duality Space
We show that the simplicial chains, C•X, on a compact, triangulated, and oriented Poincaré duality space, X, of dimension d, can be endowed with an A∞ Poincaré duality structure. Using this, we show that the shifted Hochschild cohomology, HH(CX, C•X)[d], of the cochain algebra, CX, with values in the chains, C•X, has a BV structure. This is achieved by using the A∞ Poincaré duality structure to...
متن کاملOn the Hochschild Cohomology of Tame Hecke Algebras
In this paper we are interested in Hochschild cohomology of finite-dimensional algebras; the main motivation is to generalize group cohomology to larger classes of algebras. If suitable finite generation holds, one can define support varieties of modules as introduced by [SS]. Furthermore, when the algebra is self-injective, many of the properties of group representations generalize to this set...
متن کاملThe Bv Algebra on Hochschild Cohomology Induced by Infinity Inner Products
Abstract. We define a BV-structure on the Hochschild-cohomology of a unital, associative algebra A with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomolog...
متن کاملHochschild Cohomology of Algebras of Quaternion Type, I: Generalized Quaternion Groups
In terms of generators and defining relations, a description is given of the Hochschild cohomology algebra for one of the series of local algebras of quaternion type. As a corollary, the Hochschild cohomology algebra is described for the group algebras of generalized quaternion groups over algebraically closed fields of characteristic 2. Introduction Let R be a finite-dimensional algebra over a...
متن کامل