Related papers: Linear representation of Abel-Grassmann groups
It is shown, that the mapping class group of a surface of the genus g > 1 admits a faithful representation into the matrix group GL (6g-6, Z). The proof is based on a categorical correspondence between the Riemann surfaces and the so-called…
We calculate extensions between certain irreducible admissible representations of p-adic groups.
We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…
Given a commutative unital ring $R$, we show that the finiteness length of a group $G$ is bounded above by the finiteness length of the Borel subgroup of rank one $\mathbf{B}_2^\circ(R)=\left( \begin{smallmatrix} * & * \\ 0 & *…
An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. The group ring $RG$ of a finite group $G$ is isomorphic to the set of {\em group ring matrices} over $R$. It is shown that…
We develop a general framework for studying Abelian categories arising in isomeric representation theory, that is, representation theory broadly related to the supergroup Q(n). In this first part, we introduce notions of isomeric Heisenberg…
Presentations for the holomorphs of abelian groups of the form $C_{p^n} \times 1^{m}$ for $p$=2 or an odd prime are given. These presentations extend the results given in Burnside's well-known text on finite groups on the holomorphs for the…
We classify, up to isomorphism and up to equivalence, involutions on graded-division finite-dimensional simple real (associative) algebras, when the grading group is abelian.
Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A…
We find an upper bound for the number of groups of order $n$ up to isomorphism in the variety $G = A_pA_qA_r$, where $p$, $q$ and $r$ are distinct primes. We also find a bound on the orders and on the number of conjugacy classes of…
This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite…
In recent years, there has been considerable success in computing Ext-groups of modular representations associated to the general linear group by relating this problem to one of computing Ext-groups in functor categories. In this paper, we…
We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split…
We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of linear groups, and obtain new examples of finitely generated…
In this paper we formulate and study the problem of representing groups on graphs. We show that with respect to polynomial time turing reducibility, both abelian and solvable group representability are all equivalent to graph isomorphism,…
We characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of…