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Noncommutative tori and their crossed products by finite groups
비가환 원환체와 유한군에 의한 교차곱

DC Field Value Language
dc.contributor.advisor정자아-
dc.contributor.author이재협-
dc.date.accessioned2017-07-14T00:41:24Z-
dc.date.available2017-07-14T00:41:24Z-
dc.date.issued2015-02-
dc.identifier.other000000025309-
dc.identifier.urihttps://hdl.handle.net/10371/121290-
dc.description학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 2. 정자아.-
dc.description.abstractWe study canonical group actions on higher dimensional noncommutative tori which generalize the SL2(Z) actions on 2-dimensional noncommutative tori, namely, rotation algebras and show that the crossed products of higher
dimensional simple tori by canonical actions of finite groups are not necessarily AF algebras but AT algebras. This result on non-AF crossed products is contrasted with the recently known fact that the crossed products
of irrational rotation algebras by finite subgroups of SL2(Z) are always AF aglebras.
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dc.description.tableofcontents1 Introduction 1
1.1 SL2(ℤ) actions on rotation algebras 1
1.2 Structure of the crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ) 3
1.3 Brief overview of the thesis 5
2 Noncommutative tori and Canonical actions 9
2.1 Twisted group algebras of discrete groups 9
2.2 Noncommutative tori 11
2.3 Canonical actions on noncommutative tori 16
3 Canonical actions of finite cyclic groups 22
3.1 Companion matrices of cyclotomic polynomials 23
3.2 Noncommutative tori admitting canonical actions by finite cyclic groups 26
3.3 Canonical actions on 3-dimensional simple tori by finite cyclic groups 30
4 Crossed products of noncommutative simple tori by canonical actions of finite groups 34
4.1 Structure of the crossed products of simple tori by canonical actions of finite groups 35
4.1.1 Tracial rank of crossed products 35
4.1.2 The Universal Coefficient Theorem for crossed products 37
4.1.3 Classification theorem for crossed products 39
4.2 K-theory of the crossed products 41
4.2.1 Conjugation actions free outside the origin 42
4.2.2 A sufficient condition for K1(C*(ℤd ⋊α ℤn)) 6= 0 44
4.2.3 Beyond Cn 51
5 Noncommutative simple tori on which finite cyclic groups act canonically 54
5.1 Existence of noncommutative simple tori admitting canonical actions by finite cyclic groups 55
5.2 Noncommutative simple tori admitting canonical actions by finite cyclic groups of prime orders 57
5.3 Canonical actions on 4-dimensional simple tori Αθ⊗Αθ 62
Abstract (in Korean) 70
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dc.formatapplication/pdf-
dc.format.extent1148146 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subject비가환 원환체-
dc.subject군작용-
dc.subject$C^*$-교차곱-
dc.subjectAF 대수-
dc.subject.ddc510-
dc.titleNoncommutative tori and their crossed products by finite groups-
dc.title.alternative비가환 원환체와 유한군에 의한 교차곱-
dc.typeThesis-
dc.contributor.AlternativeAuthorJae Hyup Lee-
dc.description.degreeDoctor-
dc.citation.pagesiii, 70-
dc.contributor.affiliation자연과학대학 수리과학부-
dc.date.awarded2015-02-
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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