Derived Representation Schemes and Cyclic Homology

By Y. Berest, G. Khachatryan, A. Ramadoss. 2011

48 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6b9a8b91fafbc8708d7b1fb6ea88a87fd3e813fa