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UNBOUNDED DERIVATIONS IN ALGEBRAS ASSOCIATED WITH MONOTHETIC GROUPS

Published online by Cambridge University Press:  13 January 2020

SLAWOMIR KLIMEK
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202, USA e-mail: [email protected]
MATT McBRIDE*
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, 175 President’s Cir., Mississippi State, MS 39762, USA

Abstract

Given an infinite, compact, monothetic group $G$ we study decompositions and structure of unbounded derivations in a crossed product $\text{C}^{\ast }$-algebra $C(G)\rtimes \mathbb{Z}$ obtained from a translation on $G$ by a generator of a dense cyclic subgroup. We also study derivations in a Toeplitz extension of the crossed product and the question whether unbounded derivations can be lifted from one algebra to the other.

MSC classification

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by L. O. Clark

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