 
Summary: COLLOQUIUM
University of Regina
Department of Mathematics and Statistics
Speaker: Doug Farenick (University of Regina)
Title: Specht's Theorem in Finite Factors
Date: Friday, October 26, 2007
Time: 3:30
Place: Math & Stats Lounge (CW 307.20)
Abstract
A finite factor is a von Neumann algebra M of operators acting on a
complex Hilbert space such that M has trivial centre and M has a (normal,
faithful) trace functional. The most familiar example is M = Mn, the
algebra of n × n complex matrices. In this case, the trace of a matrix is the
sum of the diagonal elements, normalised so that the trace of the identity
matrix is 1. However, there are other natural examples of finite factors M
in which M has infinite dimension.
A beautiful theorem of W. Specht from the 1930s uses the trace func
tional to give a countable set of invariants that completely determines the
unitary equivalence class of a complex matrix. (This is important because
there is no canonical form for matrices under unitary equivalence.) In this
