Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Characteristic principal bundles

Author: Harvey A. Smith
Journal: Trans. Amer. Math. Soc. 211 (1975), 365-375
MSC: Primary 22D25; Secondary 55F10
MathSciNet review: 0376953
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Characteristic principal bundles are the duals of commutative twisted group algebras. A principal bundle with locally compact second countable (Abelian) group and base space is characteristic iff it supports a continuous eigenfunction for almost every character measurably in the characters, also iff it is the quotient by Z of a principal E-bundle for every E in $ {\operatorname{Ext}}(G,Z)$ and a measurability condition holds. If a bundle is locally trivial, n.a.s.c. for it to be such a quotient are given in terms of the local transformations and Čech cohomology of the base space. Although characteristic G-bundles need not be locally trivial, the class of characteristic G-bundles is a homotopy invariant of the base space. The isomorphism classes of commutative twisted group algebras over G with values in a given commutative $ {C^\ast}$-algebra A are classified by the extensions of G by the integer first Čech cohomology group of the maximal ideal space of A.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22D25, 55F10

Retrieve articles in all journals with MSC: 22D25, 55F10

Additional Information

Article copyright: © Copyright 1975 American Mathematical Society