nLab derived representation scheme

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