Algebra, Logic and Topology

 

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Title
Quantal spaces

Abstract
One of the principal reasons for the introduction of the concept of quantale was to find a categorical context, generalising to the non-commutative case that of locales, within which the insights of Giles and Kummer into the spectral representation of C*-algebras might be placed. Consideration of their ideas led to the concept of the spectrum Max A of any C*-algebra A , functorial on the category of C*-algebras and admitting a Gelfand-Naimark representation exactly generalising that in the commutative case. The question remained of whether this spectrum Max A could be considered in some sense to be a quantal space. Approaching from the classical belief that its points should be the equivalence classes of irreducible representations, one may obtain a concept of a point of an involutive quantale which satisfies this criterion, yet extends that of a point of a locale. Generalising again the situation for locales, one may characterise those involutive quantales that are spatial as those having enough points, arriving finally at the concept of a quantal space.

Speaker(s)
Christopher Mulvey (University of Sussex, UK)

Date
February 09, 2001

Time
15.00

Room
5.5

 
     
 

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