Related papers: Various Representation Dimensions associated with …

In this paper, we study good semigroups of \mathbb{N}^n, a class of semigroups that contains the value semigroups of algebroid curves with n branches. We give the definition of embedding dimension of a good semigroup showing that, in the…

Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…

In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.

We explore the implications of the finiteness of homological dimensions for Ext modules, focusing on projective dimension, injective dimension, and their Gorenstein counterpart. In this direction, we establish several finiteness criteria…

Superspecies are introduced to provide the nice constructions of all finite-dimensional superalgebras. All acyclic superspecies, or equivalently all finite-dimensional (gr-basic) gr-hereditary superalgebras, are classified according to…

We provide a simple method to compute upper bounds on the essential dimension of split reductive groups with finite or connected center by means of their generically free representations. Combining our upper bound with previously known…

We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made…

We define a numerical quasi-isometry invariant of a finitely generated group, whose values parametrize the difference between the group being uniformly embeddable in a Hilbert space and the reduced C*-algebra of the group being exact.

In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…

We classify representations of the mapping class group of a surface of genus $g$ (with at most one puncture or boundary component) up to dimension $3g-3$. Any such representation is the direct sum of a representation in dimension $2g$ or…

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

Let $k$ be a commutative Noetherian ring and $\underline{\mathscr{C}}$ be a locally finite $k$-linear category equipped with a self-embedding functor of degree 1. We show under a moderate condition that finitely generated torsion…

We study the structure of the category of integrable level zero representations with finite dimensional weight spaces of affine Lie algebras. We show that this category possesses a weaker version of the finite length property, namely that…

Let $\Gamma$ be a finite group and $V$ a finite-dimensional $\Gamma$-graded space over an algebraically closed field of characteristic not equal to 2. In the sense of conjugation, we classify all the so-called pre-nil or nil maximal abelian…

Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…

We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we…