Derived representation schemes and cyclic homology

作者：Berest Yuri^*; Khachatryan George; Ramadoss Ajay

来源：Advances in Mathematics, 2013, 245: 625-689.

DOI：10.1016/j.aim.2013.06.020

• Noncommutative geometry
• Derived moduli space
• Cyclic homology
• Representation variety
• Higher trace map
• Lie algebra homology

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.

• 出版日期2013-10-1