Linear groups associated with elements of a group algebra

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

C*-Algebra numerical range of quadratic elements

It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Linear Groups and Group Rings

This paper consists of two parts. The first is concerned with free products in linear groups and uses the usual “ping pong” lemma and attractors to prove the results. What is new here is that we allow certain subspaces of V associated with the semisimple and generalized transvection operators to have dimensions larger than 1. The second part is concerned with applications of this machinery to i...

Invariant elements in the dual Steenrod algebra

‎In this paper‎, ‎we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${mathcal{A}_p}^*$ under the conjugation map $chi$ and give bounds on the dimensions of $(chi-1)({mathcal{A}_p}^*)_d$‎, ‎where $({mathcal{A}_p}^*)_d$ is the dimension of ${mathcal{A}_p}^*$ in degree $d$‎.