We characterize rings R in which certain elements x have the property that CR(x) (resp. the set of zero divisors in CR(x)) is finite. We also explore the consequences of an assumption that certain x satisfy CR(x) = 〈x〉.

This paper discusses a computational problem arising in the study of the structure theory of Brauer's orthogonal and symplectic centralizer algebras. The problem is to compute the ranks of certain combinatorially defined matrices Zm k(x) (these matrices are presented in §2). This computation is difficult because the sizes of the matrices Zm k(x) are enormous even for small values of m and k . H...

Let F be an algebraically closed field and let G be a semisimple F-algebraic group for which the characteristic of F is very good. If X ∈ Lie(G) = Lie(G)(F) is a nilpotent element in the Lie algebra of G, and if C is the centralizer in G of X, we show that (i) the root datum of a Levi factor of C, and (ii) the component group C/Co both depend only on the Bala-Carter label of X; i.e. both are in...

Let R be a ring with involution. An additive mapping T : R → R is called a left ∗-centralizer (resp. Jordan left ∗-centralizer) if T (xy) = T (x)y∗ (resp. T (x2) = T (x)x∗) holds for all x, y ∈ R, and a reverse left ∗-centralizer if T (xy) = T (y)x∗ holds for all x, y ∈ R. The purpose of this paper is to solve some functional equations involving Jordan left ∗-centralizers on some appropriate su...

Let G be a compact connected Lie group andH the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan