Related papers: On algebras generated by positive operators

In this paper the authors seek to trace in an accessible fashion the rapid recent development of the theory of the matrix geometric mean in the cone of positive definite matrices up through the closely related operator geometric mean in the…

We present a new look at description of real finite-dimensional Lie algebras. The basic element turns out to be a pair $(F,v)$ consisting of a linear mapping $F\in End(V)$ and its eigenvector $v$. This pair allows to build a Lie bracket on…

Given a direct sum $A$ of full matrix algebras, if there is a combinatorial interpretation associated with both the dimension of $A$ and the dimensions of the irreducible $A$-modules, then this can be thought of as providing an analogue of…

Let $A$ be a Banach algebra with a bounded left approximate identity $\{e_\lambda\}_{\lambda\in\Lambda}$, let $\pi$ be a continuous representation of $A$ on a Banach space $X$, and let $S$ be a non-empty subset of $X$ such that…

We consider algebras with basis numerated by elements of a group $G.$ We fix a function $f$ from $G\times G$ to a ground field and give a multiplication of the algebra which depends on $f$. We study the basic properties of such algebras. In…

Given a variety of algebras V, we study categories of algebras in V with a compatible structure of uniform space. The lattice of compatible uniformities of an algebra, Unif A, can be considered a generalization of the lattice of congruences…

Let ${\bf M}_n(\mathbb{F})$ be the algebra of $n\times n$ matrices over an arbitrary field $\mathbb{F}$. We consider linear maps $\Phi: {\bf M}_n(\mathbb{F}) \rightarrow {\bf M}_r(\mathbb{F})$ preserving matrices annihilated by a fixed…

Theorem 7 in Ref. [Linear Algebra Appl., 430, 1-6, (2009)] states sufficient conditions to determine whether a pair generates the algebra of 3x3 matrices over an algebraically closed field of characteristic zero. In that case, an explicit…

Inductive algebras for the irreducible unitary representations of the universal cover of the group of unimodular two by two matrices are classified. The classification of homogeneous shift operators is obtained as a direct consequence. This…

Let $E$ be a two-dimensional \'etale algebra over a non-Archimedean local field $K$ of characteristic zero. We show that the unitary group of a non-degenerate hermitian lattice over $E$ is generated by symmetries and rescaled Eichler…

A dimension group is a partially ordered countable group such that (1) every finite subset is contained in an ordered subgroup which is a finite direct power of Z and (2) the group has an order unit i.e. a positive element u such that every…

Hilbert's ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic polynomials. We give a linear-algebraic approach to…

Fix a commutative monoid $(T,+,0)$, a commutative monoid $(\Gamma,+,0_\Gamma)$, and a map \[ (a,\alpha,b,\beta,c)\longmapsto a\,\alpha\,b\,\beta\,c\in T \] which is additive in each variable and associative in the ternary sense. A left…

We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with $\mathbb{C}$ and that their characters satisfy orthogonality relations. Then…

We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting…

A code algebra $A_C$ is a non-associative commutative algebra defined via a binary linear code $C$. We study certain idempotents in code algebras, which we call small idempotents, that are determined by a single non-zero codeword. For a…

In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find a system of parameters for the coordinate rings of these two sets and their…

Let A be an algebra whose group of units U(A) satisfies a Laurent polynomial identity (LPI). We establish conditions on these polynomials in such a way that nil-generated algebras and group algebras with torsion groups over infinite fields…

We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra $\mathfrak{g}$. The Lie algebra generators are represented…

We prove that all definable pre-orders are atomic, in a finitely generated free algebra of a discriminator variety of finite similarity type which is generated by its finite members.