Derived Representation Schemes and Cyclic Homology

2011/12/07 by Berest, Yuri, Khachatryan, George, Ramadoss, Ajay · 1 citation
#FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1112.1449

Abstract

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) → H_n[DRep_V(A)], extending the canonical trace Tr_V(A): HC₀(A) → 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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