Abstract
Let \({\mathbb{M}}=P\times {M}\) be a variable Mautner group. We describe the \(C^*\)-algebra \(C^*({\mathbb{M}})\) of \({\mathbb{M}}\) in terms of an algebra of operator fields defined over \(P\times {{\mathbb{C}}^2} .\)
Similar content being viewed by others
References
Boidol, J., Leptin, H., Schürmann, J., Vahle, D.: Räume primitiver Ideale von Gruppenalgebren. Math. Ann. 236, 1–13 (1978)
Boidol, J.: *-Regularity of some classes of solvable groups. Math. Ann. 261, 477–481 (1982)
Dixmier, J.: Les \(C^*\)-algèbres et Leurs Reprèsentations. (French) Deuxième édition Cahiers Scientifiques, Fasc. XXIX Gauthier-Villars Éditeur, Paris 1969 xv+390 pp. 46.65
Leptin, H., Ludwig, J.: Unitary representation theory of exponential Lie groups. De Gruyter Expositions in Mathematics, 18. Walter de Gruyter & Co., Berlin, 1994. x+200 pp.
Lin, Y.-F., Ludwig, J.: The C*-algebra of \(ax+b\)-like groups. J. Funct. Anal. 259, 104–130 (2010)
Ludwig, J.: Dual topology of diamond groups. Journal für die reine und angewandte Mathematik 467, 67–88 (1995)
Sudo, T.: Structure of group C*-algebras of the generalized Mautner groups. J. Math. Kyoto Univ. (JMKYAZ) 42(2), 393–402 (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Michael Frank.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Regeiba, H. The \(C^*\)-algebra of the variable Mautner group. Banach J. Math. Anal. 16, 65 (2022). https://doi.org/10.1007/s43037-022-00219-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s43037-022-00219-0