Journal of the Mathematical Society of Japan

A class of almost $C_0({\cal K})$-C*-algebras

Junko INOUE, Ying-Fen LIN, and Jean LUDWIG

Full-text: Open access


We consider in this paper the family of exponential Lie groups $G_{n,\mu}$, whose Lie algebra is an extension of the Heisenberg Lie algebra by the reals and whose quotient group by the centre of the Heisenberg group is an $ax+b$-like group. The C*-algebras of the groups $G_{n,\mu}$ give new examples of almost $C_0({\cal K})$-C*-algebras.

Article information

J. Math. Soc. Japan, Volume 68, Number 1 (2016), 71-89.

First available in Project Euclid: 25 January 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
Secondary: 22E25: Nilpotent and solvable Lie groups 22E27: Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)

C*-algebra exponential Lie group algebra of operator fields


INOUE, Junko; LIN, Ying-Fen; LUDWIG, Jean. A class of almost $C_0({\cal K})$-C*-algebras. J. Math. Soc. Japan 68 (2016), no. 1, 71--89. doi:10.2969/jmsj/06810071.

Export citation


  • R. J. Archbold, J. Ludwig and G. Schlichting, Limit sets and strengths of convergence for sequences in the duals of thread-like Lie groups, Math. Z., 255 (2007), 245–282.
  • J. M. G. Fell, The structure of algebras of operator fields, Acta Math., 106 (1961), 233–280.
  • R.-Y. Lee, On the C* algebras of operator fields, Indiana Univ. Math. J., 26 (1977), 351–372.
  • H. Leptin and J. Ludwig, Unitary representation theory of exponential Lie groups, De Gruyter Expositions in Math., 18, 1994.
  • Y.-F. Lin and J. Ludwig, The C*-algebras of $ax+b$-like groups, J. Funct. Anal., 259 (2010), 104–130.
  • Y.-F. Lin and J. Ludwig, An isomorphism between group C*-algebras of $ax+b$-like groups, Bull. London Math. Soc., 45 (2013), 257–267.
  • J. Inoue, Y.-F. Lin and J. Ludwig, The solvable Lie group $N_{6,28}$: an example of an almost $C_0(\K)$-C*-algebra, Adv. Math., 272 (2015), 252–307.
  • J. Ludwig and L. Turowska, The C*-algebras of the Heisenberg group and of thread-like Lie groups, Math. Z., 268 (2011), 897–930.