Dispersing representations of semi-simple subalgebras of complex matrices
Loading...
Date
2022-06-01
Authors
Marcoux, Laurent W.
Radjavi, Heydar
Zhang, Yuanhang
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
In this paper we consider the problem of determining the maximum dimension
of P?(A!B)P, where A and B are unital, semi-simple subalgebras of the set Mn of n⇥n
complex matrices, and P 2 M2n is a projection of rank n. We exhibit a number of
equivalent formulations of this problem, including the one which occupies the majority of
the paper, namely: determine the minimum dimension of the space A\ S−1BS, where S
is allowed to range over the invertible group GL(n,C) of Mn. This problem in turn is seen
to be equivalent to the problem of finding two automorphisms ↵ and " of Mn for which
the dimension of ↵(A)+"(B) is maximised. It is this phenomenon which gives rise to the
title of the paper.
Description
The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2022.02.017 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Keywords
maximal off-diagonal dimension, minimal intersection, semi-simple subalgebras of matrix algebras, dispersion