IJPAM: Volume 62, No. 4 (2010)

REAL RANK OF THE GROUP $C^*$-ALGEBRAS OF
LIE GROUPS

Takahiro Sudo
Department of Mathematical Sciences
Faculty of Science
University of the Ryukyus
Nishihara, Okinawa, 903-0213, JAPAN
e-mail: [email protected]


Abstract.We estimate the real rank of the group $C^*$-algebras of Lie groups. We consider separately the case of connected solvable Lie groups of type I, the case of non-compact, locally compact CCR groups such as semi-simple or reductive Lie groups, and the case of certain connected or disconnected, solvable Lie groups of non type I.

Received: June 28, 2010

AMS Subject Classification: 46L05

Key Words and Phrases: $C^*$-algebra, real rank, group $C^*$-algebra, Lie group

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 62
Issue: 4