Derived Representation Schemes and Cyclic Homology

Details Derived Representation Schemes and Cyclic Homology Derived Representation Schemes and Cyclic Homology

2011-12-07

arxiv.org/abs/1112.1449v1

Mathematics

K-Theory and Homology

55 pages

Scientific paper

We describe the derived functor $ \DRep_V(A) $ of the classical 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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