Related papers: Characterization of ($\alpha$,$\alpha$)-derivation…

This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one parameter automorphisms groups. Both of them, derivations and…

For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…

Let $G$ be a group and let $X$ be a transitive $G$-space. We classify the subsets of $X$ with respect to a translation invariant ideal $\mathcal{J}$ in the Boolean algebra of all subsets of $X$, introduce and apply the relative…

Given an infinite group $G$ and a subset $A$ of $G$ we let $\Delta(A) = {g \in G : |gA \cap A| =\infty}$ (this is sometimes called the combinatorial derivation of $A$). A subset $A$ of $G$ is called large if there exists a finite subset $F$…

Let d be a linear mapping from a unital Banach algebra A into a unital left A-module M, and w in Z(A) be a left separating point of M. We show that the following three conditions are equivalent: (i) d is a Jordan left derivation; (ii) d is…

We study automorphisms, isomorphisms, and derivations of the incidence algebra $I(X,R)$, where $X$ is preordered set and $R$ is an algebra over some commutative ring $T$.

We introduce a class of algebras over a field $\mathbb{F}$ related to directed graphs in which all edges are labeled by nonzero elements of the field $\mathbb{F}$. If all labels are different from $1$, these algebras are axial algebras. We…

For $\beta\in{\mathbb Z}$, let $G(\beta)=\langle A,B\,|\, A^{[A,B]}=A,\, B^{[B,A]}=B^\beta\rangle$ be the infinite Macdonald group, and set $C=[A,B]$. Then $G(\beta)$ is a nilpotent polycyclic group of the form $\langle…

We establish a Primitive Element Theorem for fields equipped with several commuting operators such that each of the operators is either a derivation or an automorphism. More precisely, we show that for every extension $F \subset E$ of such…

$C^*$-algebras, group algebras, and the algebra $\mathcal{A}(X)$ of approximable operators on a Banach space $X$ having the bounded approximation property are known to be zero product determined. We are interested in giving a quantitative…

In this paper, we first show that for a Banach space $X$ there is a fully order reversing mapping $T$ from ${\rm conv}(X)$ (the cone of all extended real-valued lower semicontinuous proper convex functions defined on $X$) onto itself if and…

A differential analogue of the conjecture of Reichstein, Rogalski, and Zhang in algebraic dynamics is here established: if $X$ is a projective variety over an algebraically closed field of characteristic zero which admits a global algebraic…

We say that an edge colouring breaks an automorphism if some edge is mapped to an edge of a different colour. We say that the colouring is distinguishing if it breaks every non-identity automorphism. We show that such colouring can be…

For a fixed C*-algebra A, we consider all noncommutative dynamical systems that can be generated by A. More precisely, an A-dynamical system is a triple (i,B,\alpha) where $\alpha$ is a *-endomorphism of a C*-algebra B, and i: A --> B is…

Let $G$ be a graph(directed or undirected) having $k$ number of blocks. A $\mathcal{B}$-partition of $G$ is a partition into $k$ vertex-disjoint subgraph $(\hat{B_1},\hat{B_1},\hdots,\hat{B_k})$ such that $\hat{B}_i$ is induced subgraph of…

Let $X$ be a set, $B_{X}$ denotes the family of all subsets of $X$ and $F: X \longrightarrow B_{X}$ be a set-valued mapping such that $x \in F(x)$, $sup_{x\in X} | F(x)|< \kappa$, $sup_{x\in X} | F^{-1}(x)|< \kappa$ for all $x\in X$ and…

A graph $G$ is $\alpha$-excellent if every vertex of $G$ is contained in some maximum independent set of $G$. In this paper, we characterize $\alpha$-excellent bipartite graphs, $\alpha$-excellent unicyclic graphs, $\alpha$-excellent…

Inspired by connections described in a recent paper by Mark L. Lewis, between the common divisor graph $\Ga(X)$ and the prime vertex graph $\Delta(X)$, for a set $X$ of positive integers, we define the bipartite divisor graph $B(X)$, and…

Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\epsilon}>0,…

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and…