Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Induced $C^ *$-algebras and Landstad duality for twisted coactions
HTML articles powered by AMS MathViewer

by John C. Quigg and Iain Raeburn PDF
Trans. Amer. Math. Soc. 347 (1995), 2885-2915 Request permission

Abstract:

Suppose $N$ is a closed normal subgroup of a locally compact group $G$. A coaction $:A \to M(A \otimes {C^ * }(N))$ of $N$ on a ${C^ * }$-algebra $A$ can be inflated to a coaction $\delta$ of $G$ on $A$, and the crossed product $A{ \times _\delta }G$ is then isomorphic to the induced ${C^ * }$-algebra $\text {Ind}_N^G A{\times _\epsilon }N$. We prove this and a natural generalization in which $A{ \times _\epsilon }N$ is replaced by a twisted crossed product $A{ \times _{G/N}}G$; in case $G$ is abelian, we recover a theorem of Olesen and Pedersen. We then use this to extend the Landstad duality of the first author to twisted crossed products, and give several applications. In particular, we prove that if \[ 1 \to N \to G \to G/N \to 1\] is topologically trivial, but not necessarily split as a group extension, then every twisted crossed product $A{ \times _{G/N}}G$ is isomorphic to a crossed product of the form $A \times N$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L55, 46L40
  • Retrieve articles in all journals with MSC: 46L55, 46L40
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 2885-2915
  • MSC: Primary 46L55; Secondary 46L40
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1297536-3
  • MathSciNet review: 1297536