**Kontsevich-Rosenberg principle** is a heuristic that a good analogue of a commutative geometric structure on a noncommutative space (associative algebras or related objects) should induce its classical counterpart on the associated commutative representation schemes (or derived representation schemes). An example is a double Poisson structure of Michel Van den Bergh which induces ordinary Poisson bracket on representation spaces.

- M. Kontsevich, A. Rosenberg,
*Noncommutative smooth spaces*, The Gelfand Mathematical Seminars, 1996–1999, 85–108, Gelfand Math. Sem., Birkhäuser Boston 2000; arXiv:math/9812158 (published version is slightly updated with respect to arXiv version)

This came as continuation/generalization of some ideas from

- Maxim Kontsevich,
*Formal (non)-commutative symplectic geometry*, The Gelfand Mathematical. Seminars, 1990-1992, Ed. L.Corwin, I.Gelfand, J.Lepowsky, Birkhauser 1993, 173-187, pdf

Some formalizations of the principle include so called Van den Bergh’s functor.

- 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 - David Fernández,
*The Kontsevich-Rosenberg principle for bi-symplectic forms*, arXiv:1708.02650 - Stefano D’Alesio,
*Noncommutative derived Poisson reduction*, arXiv:2012.04451 - R. Bocklandt, L. Le Bruyn,
*Necklace Lie algebras and noncommutative symplectic geometry*, Math Z 240, 141–167 (2002) doi - H. Zhao,
*Commutativity of quantization and reduction for quiver representations*, Math. Z. 301, 3525–3554 (2022). doi - Maxime Fairon, David Fernández,
*On the noncommutative Poisson geometry of certain wild character varieties*, arXiv:2103.10117;*Euler continuants in noncommutative quasi-Poisson geometry*, arXiv:2105.04858

Created on September 20, 2022 at 09:01:07. See the history of this page for a list of all contributions to it.