University of Oxford Logo University of OxfordDepartment of Computer Science - Home
On Facebook
Facebook
Follow us on twitter
Twitter
Linked in
Linked in
Flickr
Flickr
Google plus
Google plus
Digg
Digg
Pinterest
Pinterest
Stumble Upon
Stumble Upon

Oxford Quantum Talks Archive

Stably Gelfand quantales, groupoids and Cartan sub-C*-algebras

Pedro Resende, Instituto Superior Tecnico, Lisbon
Categories, Logic and Foundations of Physics V, August 2009, Imperial College London

In this talk I will describe the notion of stably Gelfand quantale, by which is meant an involutive quantale Q satisfying the condition aa*a<=a iff aa*a=a for all a in Q, and as an application I will show that to each sub-C*-algebra B of a C*-algebra A one can associate in a canonical way an etale groupoid whose unit locale is that of two-sided ideals of B. This construction is related with earlier work of Kumjian, Renault and Exel on "diagonals" of C*-algebras, and there are further applications of stably Gelfand quantales (also known by Garraway as pseudo-rightsided) in theories of sheaves on quantales.

[video] [streaming video]