Automorphisms of structural matrix algebras

Automorphisms of Operator Algebras

Automorphisms of Regular Algebras

Manin associated to a quadratic algebra (quantum space) the quantum matrix group of its automorphisms. This Talk aims to demonstrate that Manin’s construction can be extended for quantum spaces which are nonquadratic homogeneous algebras. Here given a regular Artin-Schelter algebra of dimension 3 we construct the quantum group of its symmetries, i.e., the Hopf algebra of its automorphisms. For ...

NILPOTENT GRAPHS OF MATRIX ALGEBRAS

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

On Automorphisms of Polyadic Algebras

Introduction. This paper belongs to the theory of polyadic algebras as developed by Haimos [11-15], but it has a bearing on the theory of models. Two central concepts are those of homogeneous(2) and of normal extensions of a polyadic algebra (see the beginning of §2 and of §6). These concepts bear some resemblance to concepts of the theory of algebraic extensions of fields; however, we have bee...

Nakayama automorphisms of Frobenius algebras

We show that the Nakayama automorphism of a Frobenius algebra R over a field k is independent of the field (Theorem 4). Consequently, the k-dual functor on left R-modules and the bimodule isomorphism type of the k-dual of R, and hence the question of whether R is a symmetric k-algebra, are independent of k. We give a purely ring-theoretic condition that is necessary and sufficient for a finite-...