‎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.

We prove a global fixed point theorem for the centralizer of a homeomorphism of the two dimensional disk D that has attractor-repeller dynamics on the boundary with at least two attractors and two repellers. As one application, we show that there is a finite index subgroup of the centralizer of a pseudo-Anosov homeomorphism with infinitely many global fixed points. As another application we giv...

1.1. Let G be an almost simple complex algebraic group, and let GrG be its affine Grassmannian. Recall that if we set O = C[[t]], F = C((t)), then GrG = G(F)/G(O). The equivariant cohomology ring H• G(O)(GrG,C) = H • G(O)(GrG) was computed by V. Ginzburg [7] in terms of the Langlands dual group Ǧ. More precisely, let ǧ be the Lie algebra of Ǧ, and let Zǧǧ be the universal centralizer: if we den...

Using the gauge transformations of the Classical Dynamical YangBaxter Equation introduced by P. Etingof and A. Varchenko in [EV], we reduce the classification of dynamical r-matrices on a commutative subalgebra l of a Lie algebra g to a purely algebraic problem under the assumption that l admits a g-invariant complement, where g is the centralizer of l. We then describe, for a simple complex Li...

Given an n×n matrix c over a unitary ring R, the centralizer of in full Mn(R) is called principal ring, denoted by Sn(c,R). We investigate its structure and prove: (1) If invertible with c-free point, or if R has no zero-divisors Jordan-similar all eigenvalues center then separable Frobenius extension Sn(c,R) sense Kasch. (2) integral domain matrix, cellular R-algebra Graham Lehrer. In particul...