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SUMMARY:C*-algebras of submonoids of the Thompson group $F$ - Marcelo Laca
  (University of Victoria)
DTSTART:20250717T150500Z
DTEND:20250717T154500Z
UID:TALK233116@talks.cam.ac.uk
DESCRIPTION:We consider the Thompson group $F$ given by its infinite prese
 ntation$$F = \\big\\langle x_0\, x_1\, x_2\, \\ldots \\mid \\ x_jx_i=x_ix_
 {j+1}\\ {\\rm for } \\ j>i\\big\\rangle.$$&nbsp\;and study the Toeplitz C*
 -algebras ${\\cal T}_\\lambda(M_k)$ of the submonoids $P_k$ of $F$ generat
 ed by the first $k+1$ generators. We obtain a spanning set\, a characteriz
 ation of faithful representations\, and we show that the boundary quotient
 s are purely infinite simple. ${\\cal T}_\\lambda(M_0)$ is the C*-algebra 
 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 ${\\cal T}_\\l
 ambda(M_2)$ follows from work of an Huef\, Nucinkis\, Sehnem and Yang. We 
 prove nuclearity of ${\\cal T}_\\lambda(M_k)$ for $k =3\, 4$ and discuss o
 ur approach to the general case using a realization 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 algebra of a C*-correspon
 dence.&nbsp\;&nbsp\;This is joint work with A. an Huef\, B. Nucinkis\, I. 
 Raeburn and C. Sehnem.
LOCATION:External
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