Hochschild duality, localization, and smash products
By M. Farinati. 2004
63 citations recorded by the source corpus.
Abstract In this work we study the class of algebras satisfying a duality property with respect to Hochschild homology and cohomology, as in [Proc. Amer. Math. Soc. 126 (1998) 1345–1348]. More precisely, we consider the class of algebras A such that there exists an invertible bimodule U and an integer number d with the property H • ( A , M ) ≅ H d − • ( A , U ⊗ A M ) , for all A-bimodules M. We show that this class is closed under localization and under smash products with respect to Hopf algebras satisfying also the duality property. We also illustrate the subtlety on dualities with smash products developing in detail the example S ( V ) # G , the crossed product of the symmetric algebra on a vector space and a finite group acting linearly on V.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5ccb200cfaa1726cb37dc1a3c954ae4c36c549c5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the Hochschild (co)homology of quantum homogeneous spaces (2008, background): “(k,B) ≃k as k-modules. Assuming these conditions, our theorem deduces a Poincar´e-type duality between Hochschild homology H•(B,·) and cohomology H•(B,·) as studied by van den Bergh in [24], see also [6, 14] for general background information: theorem 1. If B ⊂A is a smooth quantum homogeneous space”