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 …

We study the derived representation scheme DRepn (A) parametrizing the n-dimensional
representations of an associative algebra A over a field of characteristic zero. We show that …

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 …

We offer a new approach to large N limits using the Batalin-Vilkovisky formalism, both
commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem …

In this paper, we introduce and study representation homology of topological spaces, which
is a natural homological extension of representation varieties of fundamental groups. We …

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 …

We introduce a derived representation scheme associated with a quiver, which may be
thought of as a derived version of a Nakajima variety. We exhibit an explicit model for the …

Let GG be an affine algebraic group defined over a field kk of characteristic 0. We study the
derived moduli space of GG‐local systems on a pointed connected CW complex XX …

We study the derived representation scheme DRep g (a) parameterizing the representations
of a Lie algebra a in a reductive Lie algebra g. In our earlier work, we defined two canonical …