The C*-algebra of the Boidol group-Reference-Cited by-同舟云学术

The C*-algebra of the Boidol group

Published:2024-02-01 Issue:0 Volume:0 Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Lin Ying-Fen¹,Ludwig Jean²

Affiliation:

1. Mathematical Sciences Research Centre , Queen’s University Belfast , Belfast BT7 1NN , United Kingdom

2. Institut Elie Cartan de Lorraine , UMR 7502 , [ 137665]Université de Lorraine, Metz , 57045 , France

Abstract

Abstract The Boidol group is the smallest non- ∗

{\ast}

-regular exponential Lie group. It is of dimension 4 and its Lie algebra is an extension of the Heisenberg Lie algebra by the reals with the roots 1 and -1. We describe the C*-algebra of the Boidol group as an algebra of operator fields defined over the spectrum of the group. It is the only connected solvable Lie group of dimension less than or equal to 4 whose group C*-algebra had not yet been determined.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/forum-2021-0209/pdf

Reference13 articles.

1. I. Beltiţă, D. Beltiţă and J. Ludwig, Fourier transforms of C * C^{*} -algebras of nilpotent Lie groups, Int. Math. Res. Not. IMRN 2017 (2017), no. 3, 677–714.

2. J. Boidol, ∗ \ast -regularity of exponential Lie groups, Invent. Math. 56 (1980), no. 3, 231–238.

3. J. Boidol, On a regularity condition for group algebras of nonabelian locally compact groups, Harmonic Analysis (Iraklion 1978), Lecture Notes in Math. 781, Springer, Berlin (1980), 16–21.

4. J. Dixmier, C * C^{*} -Algebras, North-Holland Math. Libr. 15, North-Holland, Amsterdam, 1977.

5. J. M. G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233–280.