Theoretical Statistics and Mathematics Unit, ISI Delhi

August 3, 2011 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Sundar Shanmugasundaram,
Indian Statistical Institute, Delhi

Title:
Cuntz-Li algebras and Inverse semigroups

Abstract of Talk

Let $R$ be an integral domain such that every quotient $R/mR$ is
finite. Cuntz and Li associated a $C^{\ast}$-algebra to $R$ called the
ring $C^{\ast}$-algebra which is the $C^{\ast}$-algebra on $L^2(R)$
generated by the unitaries induced by the addition on R and the
isometries induced by the multiplication on $R.$ Cuntz and Li showed
that this algebra is simple and purely infinite.
We will show how one can apply inverse semigroups to obtain these
results. Some generalisation of these Cuntz-Li relations due to Quigg,
Landstad and Kaliszewski will be discussed.