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Finite C*-algebras associated with labeled graphs : 유한 C*-대수로서의 라벨 그래프 C*-대수
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 정자아 | - |
dc.contributor.author | 강은지 | - |
dc.date.accessioned | 2017-07-14T00:41:50Z | - |
dc.date.available | 2017-07-14T00:41:50Z | - |
dc.date.issued | 2015-08 | - |
dc.identifier.other | 000000067041 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121299 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 정자아. | - |
dc.description.abstract | We study the properties of the C*-algebras C*(E,L,B) associated to labeled spaces (E,L,B). It is shown that if C*(E,L,B) is AF, then the labeled space (E,L,B) has no loops. We also prove that some of the known equivalent conditions for usual graph C*-algebras C*(E) to be AF are not necessarily equivalent for labeled graph C*-algebras by providing examples.
For this, we use generalized Morse sequences. These examples are also shown to be non-AF simple finite C*-algebras, which contrasts with the fact that the usual simple graph C*-algebras are either AF or purely infinite. Besides, we find a sufficient condition for a labeled space (E,L,B) to give rise to an infinite C*-algebra in the sense that every nonzero hereditary C*-subalgebra of C*(E,L,B) contains an infinite projection. | - |
dc.description.tableofcontents | Abstract i
1 Introduction 1 2 Preliminaries 5 2.1 Directed graphs and their C-algebras . . . . . . . . . . . . . . . 5 2.2 Labeled spaces and their C-algebras . . . . . . . . . . . . . . . 13 2.3 Generalized Morse sequences . . . . . . . . . . . . . . . . . . . . 23 3 AF labeled graph C-algebras 28 3.1 Loops in labeled spaces . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 Labeled spaces associated with AF algebras . . . . . . . . . . . 33 4 Non-AF nite simple labeled graph C-algebras 47 4.1 Simple nite labeled graph C-algebras of generalized Morse sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5 Labeled graph C-algebras that are not nite 58 5.1 Labeled graph C-algebras whose nonzero hereditary subalgebras are all innite . . . . . . . . . . . . . . . . . . . . . . . . . 58 Abstract (in Korean) 76 Acknowledgement (in Korean) 77 ii | - |
dc.format | application/pdf | - |
dc.format.extent | 2046966 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | graph C*-algebras | - |
dc.subject | labeled graph C*-algebras | - |
dc.subject | finite C*-algebras | - |
dc.subject | AF C*-algebras | - |
dc.subject | purely infinite C*-algebras | - |
dc.subject | generalized Morse sequences | - |
dc.subject.ddc | 510 | - |
dc.title | Finite C*-algebras associated with labeled graphs | - |
dc.title.alternative | 유한 C*-대수로서의 라벨 그래프 C*-대수 | - |
dc.type | Thesis | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 72 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2015-08 | - |
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