We describe the derived functor DRep V (A) of the affine representation scheme Rep V (A)
parametrizing the representations of an associative k-algebra A on a finite-dimensional …

Some 15 years ago M. Kontsevich and A. Rosenberg proposed a heuristic principle
according to which the family of schemes {Repn (A)} parametrizing the finite-dimensional …

In this monograph, we extend S. Schwede's exact sequence interpretation of the
Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories …

Double Poisson structures (à la Van den Bergh) on commutative algebras are considered.
The main result shows that there are no non-trivial such structures on polynomial algebras of …

Let A be a Koszul (or more generally, N-Koszul) Calabi–Yau algebra. Inspired by the works
of Kontsevich, Ginzburg and Van den Bergh, we show that there is a derived …

In this paper we show that for a Koszul Calabi-Yau algebra, there is a shifted bi-symplectic
structure in the sense of Crawley-Boevey-Etingof-Ginzburg [15], on the cobar construction of …

We study general properties of Hodge-type decompositions of cyclic and Hochschild
homology of universal enveloping algebras of (DG) Lie algebras. Our construction …

GENERALIZED QUASI POISSON STRUCTURES AND NONCOMMUTATIVE INTEGRABLE
SYSTEMS Page 1 GENERALIZED QUASI POISSON STRUCTURES AND NONCOMMUTATIVE …

We introduce the notion of double Courant–Dorfman algebra and prove that it satisfies the
so-called Kontsevich–Rosenberg principle, that is, a double Courant–Dorfman algebra …

We introduce the notions of shifted bisymplectic and shifted double Poisson structures on
differential graded associative algebras, and more generally on non-commutative derived …