Property ($T$) for Groups Graded by Root Systems, Mikhail Ershov, Andrei Jaikin-Zapirain, Martin Kassabov

Автор: Pierre-Alain Cherix; Michael Cowling; Paul Jolissa
Название: Groups with the Haagerup Property
ISBN: 3034894864 ISBN-13(EAN): 9783034894869
Издательство: Springer
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Цена: 65210.00 T
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Описание: A locally compact group has the Haagerup property, or is a-T-menable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space.

Автор: Pierre-Alain Cherix; Michael Cowling; Paul Jolissa
Название: Groups with the Haagerup Property
ISBN: 3034809050 ISBN-13(EAN): 9783034809054
Издательство: Springer
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Цена: 37260.00 T
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Описание: 1 Introduction.- 1.1 Basic definitions.- 1.1.1 The Haagerup property, or a-T-menability.- 1.1.2 Kazhdan's property (T).- 1.2 Examples.- 1.2.1 Compact groups.- 1.2.2 SO(n, 1) and SU(n, 1).- 1.2.3 Groups acting properly on trees.- 1.2.4 Groups acting properly on R-trees.- 1.2.5 Coxeter groups.- 1.2.6 Amenable groups.- 1.2.7 Groups acting on spaces with walls.- 1.3 What is the Haagerup property good for?.- 1.3.1 Harmonic analysis: weak amenability.- 1.3.2 K-amenability.- 1.3.3 The Baum-Connes conjecture.- 1.4 What this book is about.- 2 Dynamical Characterizations.- 2.1 Definitions and statements of results.- 2.2 Actions on measure spaces.- 2.3 Actions on factors.- 3 Simple Lie Groups of Rank One.- 3.1 The Busemann cocycle and the Gromov scalar product.- 3.2 Construction of a quadratic form.- 3.3 Positivity.- 3.4 The link with complementary series.- 4 Classification of Lie Groups with the Haagerup Property.- 4.0 Introduction.- 4.1 Step one.- 4.1.1 The fine structure of Lie groups.- 4.1.2 A criterion for relative property (T).- 4.1.3 Conclusion of step one.- 4.2 Step two.- 4.2.1 The generalized Haagerup property.- 4.2.2 Amenable groups.- 4.2.3 Simple Lie groups.- 4.2.4 A covering group.- 4.2.5 Spherical functions.- 4.2.6 The group SU(n,1).- 4.2.7 The groups SO(n, 1) and SU(n,1).- 4.2.8 Conclusion of step two.- 5 The Radial Haagerup Property.- 5.0 Introduction.- 5.1 The geometry of harmonic NA groups.- 5.2 Harmonic analysis on H-type groups.- 5.3 Analysis on harmonic NA groups.- 5.4 Positive definite spherical functions.- 5.5 Appendix on special functions.- 6 Discrete Groups.- 6.1 Some hereditary results.- 6.2 Groups acting on trees.- 6.3 Group presentations.- 6.4 Appendix: Completely positive mapson amalgamated products, by Paul Jolissaint.- 7 Open Questions and Partial Results.- 7.1 Obstructions to the Haagerup property.- 7.2 Classes of groups.- 7.2.1 One-relator groups.- 7.2.2 Three-manifold groups.- 7.2.3 Braid groups.- 7.3 Group constructions.- 7.3.1 Semi-direct products.- 7.3.2 Actions on trees.- 7.3.3 Central extensions.- 7.4 Geometric characterizations.- 7.4.1 Chasles' relation.- 7.4.2 Some cute and sexy spaces.- 7.5 Other dynamical characterizations.- 7.5.1 Actions on infinite measure spaces.- 7.5.2 Invariant probability measures.

Автор: Ron Donagi; Mauro Francaviglia; Silvio Greco; Bori
Название: Integrable Systems and Quantum Groups
ISBN: 3540605428 ISBN-13(EAN): 9783540605423
Издательство: Springer
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Цена: 55850.00 T
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Описание: The aim of this CIME session was to review the state of the art in the development of the theory of integrable systems and their relations with quantum groups. The papers in this volume contain both a survey of problems and a number of original contributions to the subject.

Автор: Bob Oliver
Название: Reduced Fusion Systems Over 2-Groups of Sectional Rank at Most 4
ISBN: 1470415488 ISBN-13(EAN): 9781470415488
Издательство: Mare Nostrum (Eurospan)
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Цена: 78540.00 T
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Описание: The author classifies all reduced, indecomposable fusion systems over finite $2$-groups of sectional rank at most $4$. The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional $2$-rank at most $4$. But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

Автор: Alberto Ibort; M.A. Rodr?guez
Название: Integrable Systems, Quantum Groups, and Quantum Field Theories
ISBN: 9401048746 ISBN-13(EAN): 9789401048743
Издательство: Springer
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Цена: 46570.00 T
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Описание: Proceedings of the NATO Advanced Study Institute and XXIII GIFT International Seminar on `Recent Problems in Mathematical Physics`, Salamanca, Spain, June 15-27, 1992

Автор: Hazrat
Название: Graded Rings and Graded Grothendieck Groups
ISBN: 1316619583 ISBN-13(EAN): 9781316619582
Издательство: Cambridge Academ
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Цена: 60190.00 T
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Описание: This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra, and brings together results scattered across the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.

Автор: Franz G. Timmesfeld
Название: Abstract Root Subgroups and Simple Groups of Lie-Type
ISBN: 3034875967 ISBN-13(EAN): 9783034875967
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups.

Автор: Michael Aschbacher
Название: Overgroups of Root Groups in Classical Groups
ISBN: 1470418452 ISBN-13(EAN): 9781470418458
Издательство: Mare Nostrum (Eurospan)
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Цена: 96090.00 T
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Описание: The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups.