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On the homology of graded algebras
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In this paper, the components of Hochschild homology in the case of strongly G graded algebra are described in terms of a spectral sequence where Hq (R,Sg ) is the Hochhedral homology of the identity component R = Se of S with coefficients in the bimodule Sg.Abstract:
Let be an algebra that is graded by a group G. Then the Hochschild and cyclic homologies of S have canonical decompositions with components labeled by the set T(G) of conjugacy classes of G : for Hochschild homology and similarly for cyclic homology. In this article, we describe the components of Hochschild homology in the case where S is strongly G graded.The description is given in terms of a spectral sequence where Hq (R,Sg ) is the Hochschild homology of the identity component R = Se of S with coefficients in the bimodule Sg and Hp (CG (g),.) is the group homology of the centralizer CG (g) of g in G. If R is a separable algebra then the spectral sequence degenerates and yields an isomorphismread more
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TL;DR: In this article, the category of matrix factorizations for an isolated hypersurface singularity was studied and the canonical bilinear form on the Hochschild homology of this category was computed.
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TL;DR: In this article, the Hochschild homology and cohomology groups of the invariant algebra A n (C ) G were computed for a finite subgroup of Sp (2 n, C ) acting by automorphisms in the Weyl algebra.
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Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations
TL;DR: In this paper, the category of matrix factorizations for an isolated hypersurface singularity was studied and the canonical bilinear form on the Hochschild homology of this category was computed.
References
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Book
Cohomology of Groups
TL;DR: In this paper, an advanced textbook introduces students to cohomology theory and no knowledge of homological algebra is assumed beyond what is normally taught in a first course in algebraic topology.
Journal ArticleDOI
Sur quelques points d'algèbre homologique, I
Book
A Course in Homological Algebra
Peter Hilton,Urs Stammbach +1 more
TL;DR: In this paper, the authors propose an extension of the Kunneth Theorem for Abelian groups, which is based on the notion of double complexes, and they use it to define the (co-)homology of groups.
Journal ArticleDOI
Cyclic homology and the Lie algebra homology of matrices.
Jean-Louis Loday,Daniel Quillen +1 more