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Twisted Partial Actions: A Classification of Regular C*‐Algebraic Bundles
Author(s) -
Exel R
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000154
Subject(s) - mathematics , semidirect product , bundle , unit (ring theory) , algebra over a field , pure mathematics , product (mathematics) , countable set , mathematics subject classification , group (periodic table) , action (physics) , algebraic number , mathematical analysis , geometry , chemistry , materials science , mathematics education , organic chemistry , physics , quantum mechanics , composite material
We introduce the notion of continuous twisted partial actions of a locally compact group on a C*‐algebra. With such, we construct an associated C*‐algebraic bundle called the semidirect product bundle. Our main theorem shows that, given any C*‐algebraic bundle which is second countable and which satisfies a certain regularity condition (automatically satisfied if the unit fibre algebra is stable), there is a continuous twisted partial action of the base group on the unit fibre algebra, whose associated semidirect product bundle is isomorphic to the given one. 1991 Mathematics Subject Classification : 46L05, 46L40, 46L55.