[Binghamton Geometry/Topology Seminar] October 16

[Marco Varisco]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR
  http://www.math.binghamton.edu/dept/topsem/

Date:  Thursday, October 16, 2008

Time:  2:50 pm

Place:  Library North 2205
  (followed by coffee/tea in the Anderson Reading Room)

Speaker:  Gabriel Picioroaga (Binghamton University)

Title:  Representations of Thompson's group F in L^2(R^n)

Abstract:  We study faithful unitary representations of Thompson's
group F in L^2(R^n). The amenability question of F is translated
within this framework in terms of weak containments with respect to
the left regular representation. We prove that the extension of each
representation to the universal group algebra has non-trivial kernel.
Our main result says that the direct sum of all representations weakly
contains the left regular representation. We discuss the relevance of
this result to the amenability problem of F: for example, the lack of
projections of the reduced C*-algebra generated by F should transfer
to the C*-algebras generated by the above representations. Moreover,
this result could allow for other C*-algebraic invariants to be
tested.