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...

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.

A new class of locally unital and finite dimensional algebras over an arbitrary algebraically closed field is discovered. Each them admits upper weakly triangular decomposition, a generalization split decomposition. It established that the category -lfdmod left -modules fully stratified in sense Brundan-Stroppel. Moreover, semisimple if only its centralizer subalgebras associated to certain ide...

For a monoid M of k-valued unary operations, the centralizer M∗ is the clone consisting of all k-valued multi-variable operations which commute with every operation in M . First we give a sufficient condition for a monoid M to have the least clone as its centralizer. Then using this condition we determine centralizers of all monoids containing the symmetric group. AMS Mathematics Subject Classi...

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...

In this paper, we define the non-centralizer graph associated to a finite group G, as the graph whose vertices are the elements of G, and whose edges are obtained by joining two distinct vertices if their centralizers are not equal. We denote this graph by ΥG. The non-centralizer graph is used to study the properties of the non-commuting graph of an AC-group. We prove that the non-centralizer g...

The centralizer C(w) of an elliptic element w in a Weyl group has a natural symplectic representation on the group of w-coinvariants in the root lattice. We give the basic properties of this representation, along with applications to p-adic groups—classifying maximal tori and computing inducing data in L-packets—as well as to elucidating the structure of the centralizer C(w) itself. We give the...

Let g be a real semisimple Lie algebra and θ a fixed Cartan involution of g. In this paper the subscript C is used for indicating the complexification of a real object. Denote the universal enveloping algebra of the complex Lie algebra gC by U(gC), the center of U(gC) by Z(gC), and the symmetric algebra of gC by S (gC). Similar notation is used for other complex Lie algebras or vector spaces. L...

LetG be a compact Lie group. LetM be a smoothG-manifold and V → M be an oriented G-equivariant vector bundle. One defines the spaces of equivariant forms with generalized coefficients on V and M . An equivariant Thom form θ on V is a compactly supported closed equivariant form such that its integral along the fibres is the constant function 1 on M . Such a Thom form was constructed by Mathai an...