Non-Commutative Dimension for C*-Algebras
Copyright policy )Non-Commutative Dimension for C*-Algebras
This paper is a survey of real rank and topological stable rank of \(C^*\)-algebras as a non-commutative extension of the covering dimension of topological spaces and as a non-commutative complex dimension for \(C^*\)-algebras, respectively. The classes of \(C^*\)-algebras of real rank zero and topological stable rank one, which play an important role in the classification theory of simple \(C^*\)-algebras, are discussed. Formulas for extensions and tensor products, Blackadar's problem for crossed product algebras, tracial topological, rank, etc., are also considered.
- University of Oregon United States
- Ritsumeikan University Japan
C*-algebras, topological stable rank, General theory of \(C^*\)-algebras, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, real rank, \(C^*\)-algebras, covering dimension, Noncommutative topology
C*-algebras, topological stable rank, General theory of \(C^*\)-algebras, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, real rank, \(C^*\)-algebras, covering dimension, Noncommutative topology
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!