A computational approach to the Thompson group F
release_2r6h526xxrcn5efubfoaay47pi
by
S. Haagerup, U. Haagerup, M. RamirezSolano
(2014)
Abstract
Let F denote the Thompson group with standard generators A=x_0, B=x_1.
It is a long standing open problem whether F is an amenable group. By a
result of Kesten from 1959, amenability of F is equivalent to (i)
I+A+B=3 and to (ii) A+A^1+B+B^1=4, where in both
cases the norm of an element in the group ring C F is computed in
B(ℓ^2(F)) via the regular representation of F. By extensive numerical
computations, we obtain precise lower bounds for the norms in (i) and (ii),
as well as good estimates of the spectral distributions of (I+A+B)^*(I+A+B)
and of A+A^1+B+B^1 with respect to the tracial state τ on the
group von Neumann Algebra L(F). Our computational results suggest, that
I+A+B≈ 2.95 A+A^1+B+B^1≈ 3.87. It is
however hard to obtain precise upper bounds for the norms, and our methods
cannot be used to prove nonamenability of F.
In text/plain
format
Archived Files and Locations
application/pdf 777.2 kB
file_lxh7jkmtr5ft5in7yeoscyp4ja

web.archive.org (webarchive) arxiv.org (repository) 
report
Stage
submitted
Date 20140904
Version
v1
Language
en
^{?}
access all versions, variants, and formats of this works (eg, preprints)