Traces of C*-algebras of connected solvable groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:500

Article

Beltita, Ingrid¹  Beltita, Daniel¹ 

[1] Romanian Acad, Inst Math Simion Stoilow, POB 1-764, Bucharest, Romania

关键词: Solvable group;    Solvable Lie group;    Group C*-algebra;    Trace;   

DOI  :  10.1016/j.jmaa.2021.125135

来源: Elsevier

【 摘 要 】

We give an explicit description of the tracial state simplex of the C*-algebra C*(G) of an arbitrary connected, second countable, locally compact, solvable group G. We show that every tracial state of C*(G) lifts from a tracial state of the C*-algebra of the abelianized group, and the intersection of the kernels of all the tracial states of C*(G) is a proper ideal unless G is abelian. As a consequence, the C*-algebra of a connected solvable nonabelian Lie group cannot embed into a simple unital AF-algebra. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free