Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


The Brauer group of graded continuous trace $ C\sp *$-algebras

Author: Ellen Maycock Parker
Journal: Trans. Amer. Math. Soc. 308 (1988), 115-132
MSC: Primary 46L05; Secondary 16A16, 22D25, 55R10
MathSciNet review: 946434
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be a locally compact Hausdorff space. The graded Morita equivalence classes of separable, $ {{\mathbf{Z}}_2}$-graded, continuous trace $ {C^{\ast}}$-algebras which have spectrum $ X$ form a group, $ {\operatorname{GBr} ^\infty }(X)$, the infinite-dimensional graded Brauer group of $ X$. Techniques from algebraic topology are used to prove that $ {\operatorname{GBr} ^\infty }(X)$ is isomorphic via an isomorphism $ w$ to the direct sum $ \check{H}^1(X; \underline{\mathbf{Z}}_2) \oplus \check{H}^3 (X; \underline{\mathbf{Z}})$. The group $ {\operatorname{GBr} ^\infty }(X)$ includes as a subgroup the ungraded continuous trace $ {C^{\ast}}$-algebras, and the Dixmier-Douady invariant of such an ungraded $ {C^{\ast}}$-algebra is its image in $ \check{H}^3 (X; \underline{\mathbf{Z}})$ under $ w$.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L05, 16A16, 22D25, 55R10

Retrieve articles in all journals with MSC: 46L05, 16A16, 22D25, 55R10

Additional Information

PII: S 0002-9947(1988)0946434-7
Keywords: $ {C^{\ast}}$-algebra, continuous trace, graded, Brauer group, Dixmier-Douady invariant, fiber bundle, Morita equivalence
Article copyright: © Copyright 1988 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia