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arxiv: 1112.1449 · v2 · pith:7LYMT4JInew · submitted 2011-12-07 · 🧮 math.KT · math.QA· math.RA· math.RT

Derived Representation Schemes and Cyclic Homology

Yuri Berest , George Khachatryan , Ajay Ramadoss This is my paper
classification 🧮 math.KT math.QAmath.RAmath.RT
keywords homologycyclicderiveddreprepresentationdescribefunctoroperations
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We describe the derived functor DRep_V(A) of the affine representation scheme Rep_V(A), parametrizing the representations of an associative k-algebra A on a finite-dimensional vector space V. We construct the characteristic maps Tr_V(A)_n: HC_n(A) \to H_n[DRep_V(A)], extending the canonical trace Tr_V(A): HC_0(A) \to k[Rep_V(A)] to the higher cyclic homology of the algebra A, and describe a related derived version of the representation functor introduced recently by M. Van den Bergh. We study various operations on the homology of DRep_V(A) induced by known operations on cyclic and Hochschild homology of A.

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