Related papers: On defining characteristic representations of fini…

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

In this expository paper, we first review the classification of the restricted simple Lie algebras in characteristic different from 2 and 3 and then we describe their infinitesimal deformations. We conclude by indicating some possible…

We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…

Given an integer $M\geq 2$, we deploy the generating function techniques to compute the number of $M$-th roots of identity in some of the well-known finite groups of Lie type, more precisely for finite general linear groups, symplectic…

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…

We classify all finite groups that have lifting property of mod $p$ representations to mod $p^2$ representations for all prime $p$.

We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…

Over an arbitrary field of positive characteristic we construct an example of a locally finite variety of Lie algebras which does not have a finite basis of its polynomial identities. As a consequence we construct varieties of Lie algebras…

In this work, we classify all finite groups such that for every field extension F of \mathbb{Q}, F is the field of values of at most 3 irreducible characters.

We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any…

We classify the finite dimensional irreducible representations with integral central character of finite $W$-algebras $U(\mathfrak g,e)$ associated to standard Levi nilpotent orbits in classical Lie algebras of types B and C. This…

In this paper we completely characterise irreducible tensor products of representations of alternating groups in characteristic 2 of a basic spin module with an irreducible module. This completes the classification of irreducible tensor…

A classical theorem of R. Baer describes the nilpotent radical of a finite group G as the set of all Engel elements, i.e. elements y in G such that for any x in G the n-th commutator [x,y,...,y] equals 1 for n big enough. We obtain a…

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…

We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.

Let $\mathcal{G}$ be a finite group scheme over an algebraically closed field $k$ of characteristic ${\rm char}(k)=p\geq 3$. In generalization of the familiar notion from the modular representation theory of finite groups, we define the…

In this paper we explicitly compute finite bases of disjunctive identities and finite bases of regular representations for a number of interesting finite groups.

Cohen and Taylor introduced Plesken Lie algebra as certain Lie algebra constructed using finite groups. Arjun and Romeo described the linear representation of these Lie algebras induced from group representation in [1]. Hence the authors…