The following result is proved: Let R be a 2-torsion free semiprime ring, and let T : R → R be an additive mapping, related to a surjective homomorphism θ : R → R, such that 2T (x2) = T (x)θ(x) + θ(x)T (x) for all x ∈ R. Then T is both a left and a right θ-centralizer.

The main result: Let R be a 2-torsion free semiprime ring and let T : R → R be an additive mapping. Suppose that T (xyx) = xT (y)x holds for all x, y ∈ R. In this case T is a centralizer.

This paper studies a q-deformation, Br,s(q), of the walled Brauer algebra (a certain subalgebra of the Brauer algebra) and shows that the centralizer algebra for the action of the quantum group UR(gln) on mixed tensor space (R) ⊗ (Rn)∗ is generated by the action of Br,s(q) for any commutative ring R with one and an invertible element q.

We show that if Λ is a codimension-one hyperbolic attractor for a Cr diffeomorphism f , where 2 ≤ r ≤ ∞, and f is not Anosov, then there is a neighborhood U of f in Diffr(M) and an open and dense set V of U such that any g ∈ V has a trivial centralizer on the basin of attraction for Λ.

Let G be a compact connected Lie group and H, the centralizer of a one-parameter subgroup in G. Combining the ideas of Bott-Samelson resolutions of Schubert varieties and the enumerative formula on a twisted product of 2 spheres obtained in [Du2], we obtain a closed formula for multiplying Schubert classes in the flag manifold G/H. 2000 Mathematical Subject Classification: 14N15 (14M10).

Let G/H be a compact 4-symmetric space of inner type such that the dimension of the center Z(H) of H is at most one. In this paper we shall classify involutions of G preserving H for the case where dimZ(H) = 0, or H is a centralizer of a toral subgroup of G.

By studying certain kind of centralizer algebras of the affine Schur algebra S̃(n, r) we show that S̃(n, r) is Noetherian and we determine its center. Assuming n ≥ r, we show that S̃(n+ 1, r) is Morita equivalent to S̃(n, r), and the Schur functor is an equivalence under certain conditions.

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 view of the many applications of the theory of symmetric functions to representation theory it seems desirable to have a theory of symmetric functions in the spirit of Macdonald's book Mac] for Weyl groups other than the symmetric group. Our approach to this problem is to nd an algebraic structure which motivates each statement in the classical symmetric function theory. If this algebraic no...