Related papers: Frobenius Structural Matrix Algebras

Let $n$ be a positive integer and let $f_1, \ldots, f_r$ be polynomials in $n^2$ indeterminates over an algebraically closed field $K$. We describe an algorithm to decide if the invertible matrices contained in the variety of $f_1, \ldots,…

For each Frobenius algebra there is defined a skein module of surfaces embedded in a given 3-manifold and bounding a prescribed curve system in the boundary. The skein relations are local and generate the kernel of a certain natural…

We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial…

The explicit description of the Frobenius structure for the elliptic root system of type $D_4^{(1,1)}$ in terms of the characters of an affine Lie algebra of type $D_4^{(1)}$ is given.

The representation theory of finite groups began with Frobenius's factorization of Dedekind's group determinant. In this paper, we consider the case of the semigroup determinant. The semigroup determinant is nonzero if and only if the…

The classical Frobenius problem is to find the largest integer that cannot be written as a linear combination of a given set of positive, coprime integers using nonnegative integer coefficients. Prior work has generalized the classical…

We show that a structural matrix algebra $A$ is isomorphic to the endomorphism algebra of an algebraic-combinatorial object called a generalized flag. If the flag is equipped with a group grading, an algebra grading is induced on $A$. We…

An algebraic system is proposed that represent surface cobordisms in thickened surfaces. Module and comodule structures over Frobenius algebras are used for representing essential curves. The proposed structure gives a unified algebraic…

This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…

The theory of Frobenius groups with Frobenius complements of even order largely reduces to tractable algebraic number theory. If we consider only Frobenius complements with an upper bound $s$ on the number of distinct primes dividing the…

We investigate the properties of principal elements of Frobenius Lie algebras, following the work of M. Gerstenhaber and A. Giaquinto. We prove that any Lie algebra with a left symmetric algebra structure can be embedded, in a natural way,…

A braided Frobenius algebra is a Frobenius algebra with braiding that commutes with the operations, that are related to diagrams of compact surfaces with boundary expressed as ribbon graphs. A heap is a ternary operation exemplified by a…

Let $f_{1}, \ldots, f_{k}$ be polynomials defining an algebraic set in affine $n$-space over a finite field. Suppose $k>n$. We prove that there exists a system of polynomials $g_{1}, \ldots, g_{n}$, each being a linear combination with…

In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely…

We develop a theory of \emph{locally Frobenius algebras} which are colimits of certain directed systems of Frobenius algebras. A major goal is to obtain analogues of the work of Moore \& Peterson and Margolis on \emph{nearly Frobenius…

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A and B be upper triangular n-by-n matrices that (i) are not similar to direct sums of matrices of smaller…

We explicitly show that symmetric Frobenius structures on a finite-dimensional, semi-simple algebra stand in bijection to homotopy fixed points of the trivial SO(2)-action on the bicategory of finite-dimensional, semi-simple algebras,…

We categorify various finite-type cluster algebras with coefficients using completed orbit categories associated to Frobenius categories. Namely, the Frobenius categories we consider are the categories of finitely generated Gorenstein…

We study the structure of the category of graded, connected, countable-dimensional, commutative and cocommutative Hopf algebras over a perfect field $k$ of characteristic $p$. Every $p$-torsion object in this category is uniquely a direct…

In this introductory paper we study nearly Frobenius algebras which are generalizations of the concept of a Frobenius algebra which appear naturally in topology: nearly Frobenius algebras have no traces (co-units). We survey the most basic…