It has been known for a long time that the structure of a finite simple group is intimately connected with the structure of the centralizers of its involutions. An old result of Brauer and Fowler asserts, in fact, that there are at most a finite number of simple groups in which the centralizer of an involution has a given structure. A more specific, pioneering result of Brauer established that ...

Let (AS , S) be an Artin-Tits and X a subset of S ; denote by AX the subgroup of AS generated by X. When AS is of spherical type, we prove that the normalizer and the commensurator of AX in AS are equal and are the product of AX by the quasi-centralizer of AX in AS . Looking to the associated monoids A + S and A + X , we describe the quasi-centralizer of A+X in A + S thanks to results in Coxete...

After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

This is a continuation of our project which focuses on E-polynomials and the related combinatorics. A pair groups appearing in definition yields permutation group. In this paper, we determine multi-matrix structures centralizer algebras tensor representations

In this article we give an self contained existence proof for J. Conway’s sporadic simple group Co1 [4] using the second author’s algorithm [14] constructing finite simple groups from irreducible subgroups of GLn(2). Here n = 11 and the irreducible subgroup is the Mathieu group M24. From the split extension E of M24 by a uniquely determined 11-dimensional GF(2)M24module V we construct the centr...

The centralizer algebra of the action of U(n) on the real tensor powers ⊗RV of its natural module, V = Cn, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for U(n) and with the decomposition of ⊗RV into irreducible submodules is considered.

We answer in the negative a question of Hartley about representations finite groups, by constructing examples simple groups with arbitrarily large whose endomorphism ring consists just scalars. show as consequence that there are automorphisms locally group SL(∞,Fq) trivial centralizer. The smallest our is A6 q=9.

Let [Formula: see text] be a finite-dimensional simple Lie superalgebra of type text], or over text]. the simply connected semisimple algebraic group such that Suppose is nilpotent. We describe centralizer in and its center especially. also determine labeled Dynkin diagram for prove theorems relating dimension diagram.

We prove effective equidistribution, with polynomial rate, for large closed orbits of semisimple groups on homogeneous spaces, under certain technical restrictions (notably, the acting group should have finite centralizer in the ambient group). The proofs make extensive use of spectral gaps, and also of a closing lemma for such actions.