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Events for June 12, 2017 from General and Seminar calendars

Linear Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Kunal Mukherjee , Indian Institute of Technology, Madras

Title: Factoriality of q-deformed Araki-Woods von Neumann algebras

Abstract: To any strongly continuous orthogonal representation of the real numbers on a real Hilbert space $H$, Hiai constructed $q$-deformed Araki-Woods von Neumann algebras for $-1< q< 1$, which are $W^{\ast}$-algebras arising from non tracial representations of the $q$-commutation relations, the latter yielding an interpolation between the Bosonic and Fermionic statistics. We show that these von Neumann algebras are factors whenever $dim(H)\geq 3$ and for all $q\in (-1,1)$. In some cases we also determine the type of the von Neumann algebras and show that they satisfy the bicentralizer conjecture of Connes.