# Seminar at SMU 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.