2011/02/21 by Ja A Jeong, Jeong, Ja A, Sun Ho Kim +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1102.4161
arxiv created 2011/02/21 · openalex publication_date 2011/02/21 · arxiv updated 2011/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the gauge-invariant ideal structure of a C^*-algebra C^*(E,L,B) associated to a set-finite, receiver set-finite and weakly left-resolving labelled space (E,L,B), where L is a labelling map assigning an alphabet to each edge of the directed graph E with no sinks. Under the assumption that an accommodating set B is closed under taking relative complement, it is obtained that there is a one to one correspondence between the set of all hereditary saturated subsets of B and the gauge-invariant ideals of C^*(E,L,B). For this, we introduce a quotient labelled space (E,L,[B]R) arising from an equivalence relation ∼R on B and show the existence of the C^*-algebra C^*(E,L,[B]R) generated by a universal representation of (E,L,[B]R). Also the gauge-invariant uniqueness theorem for C^*(E,L,[B]R) is obtained. For simple labelled graph C^*-algebras C^*(E,L,E), where E is the smallest accommodating set containing all the generalized vertices, it is observed that if for each vertex v of E, a generalized vertex [v]l is finite for some l, then C^*(E,L,E) is simple if and only if (E,L,E) is strongly cofinal and disagreeable. This is done by examining the merged labelled graph (F,LF) of (E,L) and the common properties that C^*(E,L,E) and C^*(F,L,F) share.