## Question on Noncommutative Geometry

(extract from post elsewhere)

Now for that question: In Connes' book Noncommutative Geometry on
p51 (of the online version at
ftp://ftp.alainconnes.org/book94bigpdf.pdf )
one reads the following:

"It follows that, given a von Neumann algebra M , there exists
a canonical homomorphism \delta of R into the group
OutM = AutM / InnM (the quotient of the automorphism group
by the normal subgroup of inner automorphisms), given by
the class of \sigma^\phi _t , independently of the choice of
\phi . Thus, Ker \delta = T(M) is an invariant of M , as is
Spec \delta = S(M) = \intersection_\phi Spec \phi .

Thus von Neumann algebras are dynamical objects. Such
an algebra possesses a group of automorphism classes
parametrized by R."

This isn't the first time I've seen a group AutM / Inn M referred to as

a "dynamical object" in a similar context, and I'd be very interested
to know why. So can someone expand on the above?

One more question while I'm here (and I've asked this before but with
no significant feedback; but perhaps this time, with luck, a suitable
specialist will be tuned in).

Why does Geometric Algebra, as championed by Hestenes among
others, still seem a niche topic? If its advantages as advertised are
true - a more compact and direct formalism - it should be more
widely used instead of Clifford algebras and tensors and suchlike.

One possible reason I guess (although with no firm basis, as I'm
not an expert) is that it is somehow too self-limiting and closed,
i.e. one can get so far, with ease (by all accounts), but then no
further by any means. As I say though, that is only supposition
and may very well be rubbish.

Cheers

John R Ramsden

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