Related papers: Skew cell modules for diagram algebras

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

A sufficient condition for the simplicity of induced modules of reductive Lie algebras is given.

We explicitly construct two-sided tilting complexes corresponding to Membrillo-Hern\'{a}ndez's tree-to-star tilting complexes for generalized Brauer tree algebras.

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$. We investigate the structure properties of the endomorphism algebras of semi-tilting $A$-modules, and prove that the endomorphism algebras arising from the…

We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…

We give a new proof that the restriction of a cell module of the Hecke algebra of the symmetric group on $n$ letters, to the Hecke algebra of the symmetric group on $n-1$ letters, has a filtration by cell modules.

Cluster automorphisms have been shown to have links to the mapping class groups of surfaces, maximal green sequences and to exchange graph automorphisms for skew-symmetric cluster algebras. In this paper we aim to generalise these results…

We demonstrate how exact structures can be placed on the additive category of right operator modules over an operator algebra in order to discuss global dimension for operator algebras. The properties of the Haagerup tensor product play a…

We construct an action of a Lie algebra on the homology groups of moduli spaces of stable sheaves on K3 surfaces under some technical conditions. This is a generalization of Nakajima's construction of sl_2-action on the homology groups. In…

This paper constructs an explicit homogeneous cellular basis for the cyclotomic Khovanov--Lauda--Rouquier algebras of type $A$.

We apply the full centre construction, defined in arXiv:0908.1250, to algebras in and module categories over categories of representations of Hopf algebras. We obtain a compact formula for the full centre of a module algebra over a Hopf…

We describe the combinatorics of the cell structure of the tensor category of bimodules over a radical square zero Nakayama algebra. This accounts to an explicit description of left, right, and two-sided cells.

We give a diagrammatic calculus for the intertwiners between permutation supermodules over the Sergeev superalgebra. We also give a diagrammatic basis for the space of intertwiners between two permutation supermodules.

A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.

We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…

In this paper, we introduce Volterra evolution algebras which are evolution algebras whose structural matrices are described by skew symmetric matrices. A main result of the present paper gives a connection between such kind of algebras…

We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.

In this paper we use the Hecke algebra of type $B$ to define a new algebra $\Sch$ which is an analogue of the q-Schur algebra. We construct Weyl modules for $\Sch$ and obtain, as factor modules, a family of irreducible $\Sch$-modules over…

We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and…

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.