On small matrix subalgebras with a trivial centralizer

Matrix Units for Centralizer Algebras

We compute matrix units for Brauer’s centralizer algebras and Hecke algebras of type A. This can be used to construct a complete system of matrix units of the centralizers of tensor products of classical Lie groups (except S0(2n)) and their quantum deformations. The calculation is done by induction inspired by path models for special operator algebras. It is similar to the calculation of Young’...

Some Small-Centralizer Properties for Rings

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〉.

Open Sets of Diffeomorphisms with Trivial Centralizer in the C Topology

On the torus of dimension 2, 3, or 4, we show that the subset of diffeomorphisms with trivial centralizer in the C topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.

Polynomial Detection of Matrix Subalgebras

The double Capelli polynomial of total degree 2t is

5 M ay 2 00 7 The centralizer of a C 1 generic diffeomorphism is trivial