相关论文: Derived equivalences between symmetric special bis…
The Singer transfer provides an interesting connection between modular representation theory and the cohomology of the Steenrod algebra. We discuss a version of `Quillen stratification' theorem for the Singer transfer and its consequences.
We study certain "\sigma-commuting varieties" associated with a pair of commuting involutions of a semisimple Lie algebra $\g$. The usual commuting variety of $\g$ and commuting varieties related to one involution are particular cases of…
We completely determine the $\tau$-tilting finiteness of Borel-Schur algebras. To achieve this, we use two recently introduced techniques in silting theory: sign decomposition as introduced by Aoki, Higashitani, Iyama, Kase and Mizuno…
We give examples of finite-dimensional algebras $A$ for which the silting objects in $K^b(\mbox{proj-}A)$ are not connected by any sequence of (possibly reducible) silting mutations. The argument is based on the fact that silting mutation…
We define a new $q$-deformation of Brauer's centralizer algebra which contains Hecke algebras of type $A$ as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected…
In this paper, we give a description of the skew-symmetrizable matrices and their mutation classes which are determined by the generalized Cartan matrices of affine type.
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
In a recent article we introduced a mechanism for producing a presentation of the descent algebra of the symmetric group as a quiver with relations, the mechanism arising from a new construction of the descent algebra as a homomorphic image…
We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of `extended quivers' which are oriented hypergraphs. We describe mutations of such…
Let $Q$ be the Dynkin quiver of type $\mathbb{D}_{n}$ with linear orientation and let $Q'$ be the quiver formed by reversing the arrow at the unique source in $Q$. In this paper, we present a complete classification of both silted algebras…
This paper investigates the tilting modules of the cyclotomic q-Schur algebras, the Young modules of the Ariki-Koike algebras, and the interconnections between them. The main tools used to understand the tilting modules are contragredient…
The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called…
We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.
We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study…
The concept of modulation is generalized to pseudo-modulation and its subclasses including pre-modulation, generalized modulation and regular modulation. The motivation is to define the valued analogue of natural quiver, called {\em natural…
The class of UMP algebras arises in several classification problems in the context of derived categories of finite-dimensional algebras. In this paper we define the class of UMP algebras and develop algebraic combinatorics tools in order to…
Motivated by the study of H\"ormander's sums-of-squares operators and their generalizations, we define the convolution algebra of transverse distributions associated to a singular foliation. We prove that this algebra is represented as…
In this paper, we study structural properties of finite mutation type quivers. In particular, we obtain a characterization of finite mutation type quivers that are associated with triangulations of surfaces and give a new numerical…
We develop the theory of special biserial and string coalgebras and other concepts from the representation theory of quivers. These tools are then used to describe the finite dimensional comodules and Auslander-Reiten quiver for the…