2004/08/14 by Takeshi Katsura, Katsura, Takeshi
Mathematics · #37B99 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Primary 46L05 #Secondary 46L55
paper · pdf · doi:10.48550/arxiv.math/0408190
openalex publication_date 2004/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the ideal structures of the C^*-algebras arising from topological graphs. We give the complete description of ideals of such C^*-algebras which are invariant under the so-called gauge action, and give the condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C^*-algebras to be simple, prime or primitive. We completely determine the prime ideals, and show that most of them are primitive. Finally, we construct a discrete graph such that the associated C^*-algebra is prime but not primitive.