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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:C*-algebras of submonoids of the Thompson group $F
 $ - Marcelo Laca (University of Victoria)
DTSTART;TZID=Europe/London:20250717T160500
DTEND;TZID=Europe/London:20250717T164500
UID:TALK233116AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/233116
DESCRIPTION:We consider the Thompson group $F$ given by its in
 finite presentation$$F = \\big\\langle x_0\, x_1\,
  x_2\, \\ldots \\mid \\ x_jx_i=x_ix_{j+1}\\ {\\rm 
 for } \\ j>i\\big\\rangle.$$&nbsp\;and study the T
 oeplitz C*-algebras ${\\cal T}_\\lambda(M_k)$ of t
 he submonoids $P_k$ of $F$ generated by the first 
 $k+1$ generators. We obtain a spanning set\, a cha
 racterization of faithful representations\, and we
  show that the boundary quotients are purely infin
 ite simple. ${\\cal T}_\\lambda(M_0)$ is the C*-al
 gebra of the unilateral shift\,${\\cal T}_\\lambda
 (M_1) \\cong {\\cal TO}_2$ is known to be nuclear 
 by results of Cuntz\; and nuclearity of ${\\cal T}
 _\\lambda(M_2)$ follows from work of an Huef\, Nuc
 inkis\, Sehnem and Yang. We prove nuclearity of ${
 \\cal T}_\\lambda(M_k)$ for $k =3\, 4$ and discuss
  our approach to the general case using a realizat
 ion of ${\\cal T}_\\lambda(M_k)$ and its boundary 
 quotient $\\partial {\\cal T}_\\lambda(M_k)$ &nbsp
 \;as the Toeplitz algebra and the Cuntz--Pimsner a
 lgebra of a C*-correspondence.&nbsp\;&nbsp\;This i
 s joint work with A. an Huef\, B. Nucinkis\, I. Ra
 eburn and C. Sehnem.
LOCATION:External
CONTACT:
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