Dispersing representations of semi-simple subalgebras of complex matrices
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.
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Cite this version of the work
Laurent W. Marcoux, Heydar Radjavi, Yuanhang Zhang
(2022).
Dispersing representations of semi-simple subalgebras of complex matrices. UWSpace.
http://hdl.handle.net/10012/18284
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