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CRM - University of Ottawa Distinguished Lecture Series

TITLE:Categories of C-star algebras subject to an action of a quantum group
SPEAKER:Stanislaw Lech Woronowicz (University of Warsaw)
DATE:Vendredi, 6 Février 2015
TIME:3:30 pm
ROOM:B005
ABSTRACT:

Given \(C^*\)-algebras \(X\) and \(Y\) one may consider the C*-algebra \(X\otimes Y\). If \(X\) and \(Y\) are equipped with actions of a locally compact quantum group \(G\), then there exists unique action of \(G\) on \(X\otimes Y\) such that the natural embeddings of \(X\) and \(Y\) into \(X\otimes Y\) intertwine the actions of \(G\). In the categorical language: tensor product \(\otimes\) defines a monoidal structure on the category \(C*_G\) of all \(C^*\)-algebras equipped with the action of \(G\).

This is no longer the case if \(G\) is a quantum group. Let \(G\) be a locally compact quantum group. It turns out that the category of \(C*_G\) admits a monoidal structure satisfying certain natural conditions if and only if \(G\) is quasitriangular. The monoidal structures are in bijective correspondence with unitary \(R\)-matrices. In general the monoidal structure is not given by \(\otimes\).

About the speaker: Stanislaw Lech Woronowicz received M.S. and Ph.D. both the degrees in theoretical physics from the University of Warsaw in 1962 and in 1968 respectively. He continued as an adjunct (1968-72), an associate professor (1972-77), and a professor (1977-2011) at the faculty of Physics, University of Warsaw. He is the founder of the theory of compact quantum groups. His research interests also include non-compact quantum groups and \(C^*\)-algebras. He also became vice dean (1977-78), and the dean (1982-84) of the Faculty of Physics, University of Warsaw. He received Alfred Jurzykowski Foundation (New York) Prize for distinguished achievements in mathematical physics in 1989, Foundation for Polish Science Prize in exact sciences for the series of papers on quantum groups and \(C^*\)-algebras in 1993. He was awarded Humboldt Research Prize in 2008, and Stefan Banach Medal in 2009. He was invited twice as an invited speaker at ICMs in Warsaw in 1983, and in Kyoto in 1990. He is a full member of Polish Academy of Science since 2002, and Towarzystwo Naukowe Warszawskie since 2004.