Seminário de Álgebra  RSS

07/02/2001, 16:00 — 17:00 — Sala P3.10, Pavilhão de Matemática
, University of Sussex, Brighton

Quantal spaces

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 MaxA 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 MaxA 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.


Organizador actual: Gustavo Granja

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