Subject: categories: Re: George Mackey, 1916-2006

From: "Ronnie Brown" <[email-masked]>
Date: Sun, 26 Mar 2006 22:48:29 +0100

I met George Mackey in April 1967 at the British
Mathematical Colloquium in Swansea, where I gave an invited  talk on the
groupoid  van Kampen theorem, and I overheard some people in the common room
saying they were not completely convinced. You win some, you lose some!

But Mackey came up to me at tea and said: `That was very interesting. I have
been using groupoids for years. My name is Mackey.'

He then told me of his work in ergodic theory using `virtual groups'. It
occurred to me that if the groupoid idea can be arrived at from two quite
different directions, then there couild be more in the groupoid idea than
met the eye. It became clear that he used the action groupoid of a group
action, and this convinced me that I should add to my planned book a chapter
on covering spaces and covering groupoids.

For those who are unaware of the idea of a virtual group, Mackey's idea was
that since a transitive action of a group corresponded to a conjugacy class
of subgroups, then an ergodic action (i.e. one where the orbits are of
measure 0 or 1) should correspond to an analogous concept. His exposition
went through various phases, including a cocycle formulation, and eventually
involved the measured groupoid corresponding to an ergodic action. This
work, and that of his students, such as Arlan Ramsay, has been a foundation,
as I understand it, for much work on  the C^*-algebras of measured
groupoids.

We met a few more times, and he was always most friendly and genuine.

When I went to Bangor, Tony Seda came there from Warwick in order to help
his mother who was ill and lived in Llandudno. His  MSc project had been in
measure theory. So we agreed he should look at Mackey's work. In the end he
developed Haar measure in this area, and when I told Mackey he said *his*
student was doing the same! Tony's excellent papers in this area have
perhaps not been as well noticed  as they should, so Tony in the end moved
into theoretical computer science.

So my conclusion is that George Mackey was a great pioneer in structural
ideas in mathematics, with a broad range of interests, and a really nice
guy.

Ronnie Brown