Related papers: Effective dimension of finite semigroups
We study the category $\mathcal{A}$ of smooth semilinear representations of the infinite symmetric group over the field of rational functions in infinitely many variables. We establish a number of results about the structure of…
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…
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…
The chief aim of this paper is to describe a procedure which, given a $d$-dimensional absolutely irreducible matrix representation of a finite group over a finite field $\mathbb{E}$, produces an equivalent representation such that all…
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
In this paper, we investigate abstract homomorphism from the special linear group over complete discrete valuation rings with finite residue field, such as the ring of p-adic integers, into the general linear group over the reals. We find…
In this paper we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. We give bounds on the order, base size, minimal degree, fixity, and chief length of an arbitrary…
We obtain minimal dimension matrix representations for each indecomposable five-dimensional Lie algebra over $\R$ and justify in each case that they are minimal. In each case a matrix Lie group is given whose matrix Lie algebra provides the…
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
This paper aims to characterize the minimal dimensions and super-dimensions of faithful representations for the Heisenberg Lie superalgebras over an algebraically closed field of characteristic zero.
We study the notion of essential dimension for a linear representation of a finite group. In characteristic zero we relate it to the canonical dimension of certain products of Weil transfers of generalized Severi-Brauer varieties. We then…
The main purpose of this note is to establish the continuity of seminorms on finite-dimensional vector spaces over the real or complex numbers.
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…
We study the essential dimension of a finite group G over a field K. A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained. We also get lower bounds of…
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
We address the problem of finding necessary and sufficient conditions for an arbitrary group, not necessarily finite, to admit a faithful irreducible representation over an arbitrary field.