Let G be a connected reductive group over an algebraically closed field $\Bbbk $ . Under mild restrictions on the characteristic of , we show that any G-module with good filtration also has as module for part centralizer nilpotent element x in its Lie algebra.

A version of non-stationary normal forms theory was recently obtained by M. Guysinsky and A. Katok, which has become an important ingredient in several recent investigations of rigidity of group actions. Our main aim is to explain their results, the sub-resonance normal forms and centralizer theorems, from a differential-geometric perspective.

We construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.

Let W be a right-angled Coxeter group. We characterize the centralizer of the Coxeter element of a finite special subgroup of W. As an application, we give a solution to the generalized word problem for Inn(W ) in Aut(W ). Mathematics Subject Classification: 20F10, 20F28, 20F55

The purpose of this paper is to prove the following result: Let R be a 2torsion free semiprime ring and let T : R → R be an additive mapping, such that 2T (x) = T (x)x + xT (x) holds for all x ∈ R. In this case T is left and right centralizer.

In practice the hypothesis that x(uv) # ~(u’v) for some conjugate U’ of u is almost always satisfied. When x is faithful and u = v-r, then this just asserts that u does not belong to the center of G (though it is an easy exercise to give a direct proof of the theorem in this case). We shall derive Theorem 1 from a general result (Theorem 2) about common constituents of permutation characters. T...