Related papers: On $G$--equivariant modular categories

We give a purely geometric categorification of tensor products of finite-dimensional simple $U_q(sl_2)$-modules and $R$-matrices on them. The work is developed in the framework of category of perverse sheaves and the categorification…

We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. We resolve a serious deficit in the existing theory by constructing a good notion of equivariant presheaves, with a suitable equivariant…

We study exact module categories over the representation categories of finite-dimensional quasi-Hopf algebras. As a consequence we classify exact module categories over some families of pointed tensor categories with cyclic group of…

Given a quasiprojective algebraic variety with a reductive group action, we describe a relationship between its equivariant derived category and the derived category of its geometric invariant theory quotient. This generalizes classical…

Let V be a complex vector space with basis {x_1,x_2,...,x_n} and G be a finite subgroup of GL(V). The tensor algebra T(V) over the complex is isomorphic to the polynomials in the non-commutative variables x_1, x_2,..., x_n with complex…

Let $k$ be an algebraically closed field of characteristic $p\ge 0$. Let $G$ be an affine group scheme over $k$. We classify the indecomposable exact module categories over the rigid tensor category $\text{Coh}_f(G)$ of coherent sheaves of…

Starting with a vertex algebra $V$, a finite group $G$ of automorphisms of $V$, and a suitable collection of twisted $V$--modules, we construct (twisted) $D$--modules on the stack of pointed $G$--covers, introduced by Jarvis, Kaufmann, and…

We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all…

It is well known that the moduli space of flat connections on a trivial principal bundle MxG, where G is a connected Lie group, is isomorphic to the representation variety Hom(\pi_1(M), G)/G. For a tiling T, viewed as a marked copy of R^d,…

Let G be a unipotent algebraic group over an algebraically closed field k of characteristic p > 0 and let l be a prime different from p. Let e be a minimal idempotent in D_G(G), the braided monoidal category of G-equivariant (under…

In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with…

Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…

We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by…

Let $V$ be a simple vertex algebra of countable dimension, $G$ be a finite automorphism group of $V$ and $\sigma$ be a central element of $G$. Assume that ${\cal S}$ is a finite set of inequivalent irreducible $\sigma$-twisted $V$-modules…

Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras A_{g,n}(V) with n\in\frac{1}{T}\Z nonnegative such that A_{g,n}(V) is a quotient of A_{g,n+1/T}(V) and a pair of functors…

In this survey article we propose the notion of a bound quiver for an exact category generalising the classical concept of the Gabriel quiver and its relation for a module category as certain ring extension. The notion is motivated by joint…

We study the relationship between derived categories of factorizations on gauged Landau-Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions on the variation, we show the derived…

Let A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) are equivalent:…

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…

Let $U$ be a graded unipotent group over the complex numbers, in the sense that it has an extension $\hat{U}$ by the multiplicative group such that the action of the multiplicative group by conjugation on the Lie algebra of $U$ has all its…