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Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories
September 23-28, 2002
Fields Institute
Toronto, ON, Canada

Organizers
George Janelidze, Georgian Academy of Sciences, Bodo Pareigis, University of Munich, Walter Tholen, York University

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From algebras to quantales and back
by
Pedro Resende
Mathematics Department, IST, Lisbon

A quantale is a semigroup in the monoidal category of sup-lattices, and one can define functors from categories of algebras to quantales by taking certain subsets of the algebras, such as closed linear subspaces of a C*-algebra, K-submodules of a K-algebra, etc. A theorem of Mulvey and Pelletier states that the irreducible representations of a complex unital C*-algebra are classified by its (involutive) quantale of closed linear subspaces, and then a theorem of Giles and Kummer in functional analysis allows us to reconstruct the C*-algebra from the quantale. The aim of this talk is to explain some of the algebraic aspects behind this reconstruction and to study the extent to which it may be carried over to other kinds of algebras, including separable algebras over abstract commutative rings.

Date received: June 3, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajf-38.