Derived representation scheme $DRep_n$ is a (nonabelian) derived functor (or its geometric counterpart) of a functor $Rep_n$ which to an associative algebra $A$ assigns the affine scheme of $n$-dimensional representations of $A$.

There are several formalisms approaching such a derived functor.

- I. Ciocan-Fontanine, M. Kapranov,
*Derived Quot schemes*, Ann. Sci. ENS**34**(2001) 403–440 - Yu. Berest, X. Chen, F. Eshmatov, A. Ramadoss,
*Noncommutative Poisson structures, derived representation schemes and Calabi-Yau algebras*, Contemp. Math.**583**(2012) 219–246 arXiv:1202.2717 - Yu. Berest, G. Felder, A. Ramadoss,
*Derived representation schemes and noncommutative geometry*, arXiv:1304.5314 - George Khachatryan,
*Derived representation schemes and non-commutative geometry*, Cornell PhD thesis under guidance of Yuri Berest online - Yuri Berest, George Khachatryan, Ajay Ramadoss,
*Derived representation schemes and cyclic homology*, Adv. Math.**245,**(2013) 625–689 arXiv:1112.1449 - Yuri Berest, Giovanni Felder, Sasha Patotski, Ajay C. Ramadoss, Thomas Willwacher,
*Representation homology, Lie algebra cohomology and derived Harish-Chandra homomorphism*, J. Eur. Math. Soc. 19:9 (2017) 2811–2893 arXiv:1410.0043

Related notions: Kontsevich-Rosenberg principle

Created on September 20, 2022 at 09:57:04. See the history of this page for a list of all contributions to it.