Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space. This work explores centralizers of the action of a complex reductive Lie algebra g on tensor space of the form M ⊗ N ⊗ V ⊗k. We define the degenerate two-boundary braid group Gk and show that centrali...

A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is ‎cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq‎ ‎Z(G)$‎. ‎In this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{CAC}$-$p$-groups‎.

Given an n× n matrix A over a field F and a scalar a ∈ F , we consider the linear codes C(A, a) := {B ∈ F | AB = aBA} of length n2. We call C(A, a) a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when a = 1) is at most n, howe...

Let $F_m$ be the free metabelian Lie algebra of rank $m$ over a field $K$ characteristic 0. An automorphism $\varphi$ is called central if commutes with every inner $F_m$. Such automorphisms form centralizer $\text{\rm C}(\text{\rm Inn}(F_m))$ group Inn}(F_m)$ in Aut}(F_m)$. We provide an elementary proof to show that Inn}(F_m))=\text{\rm Inn}(F_m)$.

this is a survey article on centralizers of finite‎ ‎subgroups in locally finite‎, ‎simple groups or lfs-groups as we‎ ‎will call them‎. ‎we mention some of the open problems about‎ ‎centralizers of subgroups in lfs-groups and applications of the‎ ‎known information about the centralizers of subgroups to the‎ ‎structure of the locally finite group‎. ‎we also prove the‎ ‎following‎: ‎let $g$ be...

‎let $r$ be a ring with involution $*$‎. ‎an additive mapping $t:rto r$ is called a left(respectively right) centralizer if $t(xy)=t(x)y$ (respectively $t(xy)=xt(y)$) for all $x,yin r$‎. ‎the purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

The set of all centralizers elements in a finite group G is denoted by Cent(G) and called n-centralizer if |Cent(G)|=n. In this paper, the structure non-abelian with property that GZ(G)≅Zp2⋊Zp2 obtained. As consequence, it proved such has exactly [(p+1)2+1] element commuting conjugacy class graph completely determined.

We show there is a residual set of non-Anosov C∞ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. If M is a surface and 2 ≤ r ≤ ∞, then we will show there exists an open and dense set of of Cr Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. Additionally, we examine commuting diffeomorphisms preserving a com...