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

We establish a connection between commuting varieties $ C_g (G) $(potentially of higher
genus), which are associated with a group scheme $ G $ consisting of upper triangular …

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 introduce the\verb| Macaulay2| package\verb| RepHomology| for the computations of
representation homology of certain spaces. The main methods implement computing the …

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 …

Let g be a finite-dimensional reductive Lie algebra (over R or C), h⊆ g its Cartan
subalgebra, R⊂ h∗ a root system of g, Q= Q (R), the root lattice (spanned by R). Write the …