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Jan Cameron
Texas A&M University
Structure results for normalizers of II1 factors
November 10, 2008 4pm, 646 PGH
Abstract
It is often illuminating to study the normalizer of a
subalgebra B of a type II1 factor M; that is, to
understand the structure of the group
NM
(B) =
{ u ∈ M unitary : uBu*= B } ,
and
the von
Neumann algebra NM (B)'' it
generates. We address a few aspects of this problem. We show that
NM (B) imposes a discrete crossed product structure on
the generated von Neumann algebra. By analyzing the structure of weakly
closed
bimodules in NM (B)'', this leads to a ''Galois-type''
theorem for normalizers, in
which we find a description of the subalgebras of NM
(B)'' in terms of a unique
countable subgroup of NM (B). Implications for
inclusions B ⊆ M arising from the
crossed product, group von Neumann algebra, and tensor product
constructions will also be addressed. Our work also yields new examples of
norming subalgebras in finite von Neumann algebra B ⊆
M is a regular inclusion of II1 factors, then B
norms M.
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Last modified: April 08 2016 - 07:21:37
