Related papers: Effective dimension of finite semigroups

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…

An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.

We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite…

This paper investigates the critical group of a faithful representation of a finite group. It computes the order of the critical group in terms of the character values, and gives some restrictions on its subgroup structure. It also computes…

In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.

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…

We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…

We present various results on disconnected reductive groups, in particular about the characteristic 0 representation theory of such groups over finite fields.

This paper reviews recent results and open problems on the conductor of finite group characters, highlighting their connections to one another and to broader topics in the representation theory of finite groups.

Fixed two positive integers m and e, some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical semigroups with multiplicity m and embedding dimension e are provided. Besides, the semigroups where…

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…

In this paper, we explore when a locally finite triangulated category has dimension zero or finite representation type. We also study generation of derived categories by orthogonal subcategories.

Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…

We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…

In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…

We discuss finite local extensions of quantum field theories in low space time dimensions in connection with categorical structures and the question of modular invariants in conformal field theory, also touching upon purely mathematical…

In this paper we deal with the following problem: how does the structure of a finite semigroup $S$ depend on the probability that two elements selected at random from $S$, with replacement, define the same inner right translation of $S$. We…

We introduce a module-theoretic approach and a linear-programming method to compute the matricial dimension of numerical semigroups. We use these to compute the matricial dimension of every numerical semigroup with Frobenius number at most…