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 …

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

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 …

In this paper, we define and study derived character maps of finite-dimensional
representations of homotopy simplicial groups, which are homotopy algebras over the …

Symmetric homology is a natural generalization of cyclic homology, in which symmetric
groups play the role of cyclic groups. In the case of associative algebras, the symmetric …

We define and study (derived) character maps of finite-dimensional representations of∞–
groups. As models for∞–groups we take homotopy simplicial groups, ie the homotopy …

This thesis has four parts. In the first part, we introduce and study representation homology
of topological spaces, which is a higher homological extension of representation varieties of …

Abstract For a Koszul Artin-Schelter regular algebra (also called twisted Calabi-Yau
algebra), we show that it has a “twisted" bi-symplectic structure, which may be viewed as a …

In these expanded lecture notes of the minicourse held at the workshop on “Homotopy
algebras, deformation theory and quantization” at the Mathematical Research and …

We study the derived representation scheme $\drep_ {\g}(\fra) $ parametrizing the
representations of a Lie algebra $\fra $ in a reductive Lie algebra $\g $. We define two …