Related papers: Spaces of generators for matrix algebras with invo…

Let K be an infinite field and let R be a K-algebra endowed with a homogeneous polynomial norm N of degree n. If N satisfies a formal analogue of the Cayley-Hamilton Theorem the we will show that R is a quotient of the ring of the…

Let G(A) be an AF-algebra given by periodic Bratteli diagram with the incidence matrix A in GL(n, Z). For a given polynomial p(x) in Z[x] we assign to G(A) a finite abelian group Z^n/p(A) Z^n. It is shown that if p(0)=1 or p(0)=-1 and…

A tuple (Z_1,...,Z_p) of matrices of size r is said to be a commuting extension of a tuple (A_1,...,A_p) of matrices of size n <r if the Z_i pairwise commute and each A_i sits in the upper left corner of a block decomposition of Z_i. This…

An evolution algebra corresponds to a quadratic matrix $A$ of structural constants. It is known the equivalence between nil, right nilpotent evolution algebras and evolution algebras which are defined by upper triangular matrices $A$. We…

Let $F$ be a field of characteristic not $2$ . An associative $F$-algebra $R$ gives rise to the commutator Lie algebra $R^{(-)}=(R,[a,b]=ab-ba).$ If the algebra $R$ is equipped with an involution $*:R\rightarrow R$ then the space of the…

The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type $A_n$, by counting the mutation class of any quiver with underlying graph $A_n$. It will also follow that if $T$ and…

In this paper, we give an RTT presentation of the twisted quantum affine algebra of type $A_{2n-1}^{(2)}$ and show that it is isomorphic to the Drinfeld new realization via the Gauss decomposition of the L-operators. This provides the first…

A general unifying framework for integrable soliton-like systems on time scales is introduced. The $R$-matrix formalism is applied to the algebra of $\delta$-differential operators in terms of which one can construct infinite hierarchy of…

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…

We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically…

In this paper we study algebraic and asymptotic properties of generating sets of algebras over orders in number fields. Let $A$ be an associative algebra over an order $R$ in an algebraic number field. We assume that $A$ is a free…

We give a combinatorial algorithm for computing Zelevinsky's involution of the set of isomorphism classes of irreducible representations of the affine Hecke algebra $\H_m(t)$ when $t$ is a primitive $n$th root of 1. We show that the same…

Various subsets of the tracial state space of a unital C*-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II_1-factor representations of a class of C*-algebras considered by…

Subalgebras of upper triangular matrix algebras have played a fundamental role in the classification of minimal varieties of polynomial growth. Such classification has become a source of study in recent years since it leads to the more…

Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultameous conjugation by $GL_n$ is generated by traces of products of generic matrices. Teranishi, 1986, found a minimal system of eleven…

We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into…

Let V be an n-dimensional vector space and let On be the orthogonal group. Motivated by a question of B. Szegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society Volume 20, Number 4,…

It is known that connected translation invariant $n$-dimensional noncommutative differentials $d x^i$ on the algebra $k[x^1,\cdots,x^n]$ of polynomials in $n$-variables over a field $k$ are classified by commutative algebras $V$ on the…

We study the possible dimension vectors of indecomposable parabolic bundles on the projective line, and use our answer to solve the problem of characterizing those collections of conjugacy classes of n by n matrices for which one can find…

Let $V$ be a two-dimensional vector space over a field $\mathbb F$ of characteristic not $2$ or $3$. We show there is a canonical surjection $\nu$ from the set of suitably generic commutative algebra structures on $V$ modulo the action of…