Volodymyr Mazorchuk

Projective-injective modules, Serre functors and symmetric algebras

Abstract We describe Serre functors for (generalisations of) the category associated with a semisimple complex Lie algebra. In our approach, projective-injective modules, that is modules which are both, projective and injective, play an important role. They control the Serre functor in the case of a quasi-hereditary algebra having a double centraliser with respect to a projective-injective module whose endomorphism ring is a symmetric algebra. As an application of the double centraliser property together with our description of Serre functors, we prove three conjectures of Khovanov about the projective-injective modules in the parabolic category .

Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module

Translation and shuffling of projectively presentable modules and a categorification of the parabolic Hecke module

On the irreducible representations of a finite semigroup

Work of Clifford, Munn and Ponizovskii parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions of the irreducible representations were later obtained independently by Rhodes and Zalcstein and by Lallement and Petrich. All of these approaches make use of Reess theorem characterizing 0-simple semigroups up to isomorphism. Here we provide a short modern proof of the Clifford-Munn-Ponizovskii result based on a lemma of J. A. Green, which allows us to circumvent the theory of 0-simple semigroups. A novelty of this approach is that it works over any base ring.

Simple Virasoro modules induced from codimension one subalgebras of the positive part

We construct a new five-parameter family of simple modules over the Virasoro Lie algebra.

Cell 2-representations of finitary 2-categories

We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite-dimensional algebras. In particular, we define, construct and descri ...

Categories of Induced Modules and Standardly Stratified Algebras

We construct a generalization of the BGG-category O, whose blocks correspond to standardly stratified algebras. We prove reciprocity formulae in these categories and present two classes of examples.

Supports of weight modules over Witt algebras

In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras

Equivalence of Blocks for the General Linear Lie Superalgebra

W_n

Enright's completions and injectively copresented modules

, we explicitly describe supports of such modules. We also obtain some descriptions on the support of an arbitrary simple weight module over a

ENDOMORPHISMS OF , , AND

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