publication . Article . Preprint . 2005

On the stable rank of algebras of operator fields over metric spaces

Ping Wong Ng; Takahiro Sudo;
Open Access
  • Published: 04 Jan 2005 Journal: Journal of Functional Analysis, volume 220, pages 228-236 (issn: 0022-1236, Copyright policy)
  • Publisher: Elsevier BV
Abstract
Let G be a finitely generated, torsion-free, two-step nilpotent group. Let C^*(G) be the universal C^*-algebra of G. We show that acsr(C^*(G)) = acsr(C((\hat{G})_1)), where for a unital C^*-algebra A, acsr(A) is the absolute connected stable rank of A, and (\hat{G})_1 is the space of one-dimensional representations of G. For the case of stable rank, we have close results. In the process, we give a stable rank estimate for maximal full algebras of operator fields over a metric space.
Subjects
free text keywords: Analysis, Mathematics - Operator Algebras, 47L99, Operator Algebras (math.OA), FOS: Mathematics, C*-algebra, Stable rank, Bass stable rank, Universal C*-algebra, Discrete nilpotent group, Two-step, Continuous field, Algebra of operator fields, Representations, Nonstable K-theory, Finitely-generated abelian group, Unital, Space (mathematics), Metric space, Rank (differential topology), Nilpotent group, Operator (physics), Pure mathematics, Discrete mathematics, Mathematics, Operator algebra
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