Journal
ADVANCES IN MATHEMATICS
Volume 245, Issue -, Pages 625-689Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2013.06.020
Keywords
Noncommutative geometry; Derived moduli space; Cyclic homology; Representation variety; Higher trace map; Lie algebra homology
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Funding
- NSF [DMS 09-01570]
- Swiss National Science Foundation [PZ00P2-127427/1]
- Swiss National Science Foundation (SNF) [PZ00P2_127427] Funding Source: Swiss National Science Foundation (SNF)
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0901570] Funding Source: National Science Foundation
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We describe the derived functor DRep(nu) (A) of the affine representation scheme Rep(nu) (A) parametrizing the representations of an associative k-algebra A on a finite-dimensional vector space nu. We construct the characteristic maps Tr-nu (A)(n) : HCn (A) -> H-n[DRep(nu) (A)] extending the canonical trace Tr-nu (A) : HC0(A) -> k[Rep nu (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(nu) (A) induced by known operations on cyclic and Hochschild homology of A. (C) 2013 Elsevier Inc. All rights reserved.
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