Umfang:
Online-Ressource
,
v.: digital
Ausgabe:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
1283444526
,
9781461407096
,
9781283444521
Serie:
Springer Proceedings in Mathematics 10
Inhalt:
Annotation, These articles reflect the current major trends in research in the geometric and combinatorial aspects of study of finite simple groups, Chevalley groups and their generalisations
Inhalt:
This is the Proceedings of the ICM 2010 Satellite Conference on "Buildings, Finite Geometries and Groups" organized at the Indian Statistical Institute, Bangalore, during August 29 - 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these
Anmerkung:
International conference proceedings
,
Includes bibliographical references
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Buildings, Finite Geometries and Groups; Preface; Talks given in the Conference; Participants; Contents; On Characterizing Designs by Their Codes; 1 Introduction; 1.1 The Fundamental Principle of Coding Theory of Designs; 2 Generalized Polygons; 3 Dual Codes of 2-Designs; 4 Codes of Finite Projective Spaces; 5 Projective Planes of Prime Order; References; The Geometry of Extremal Elements in a Lie Algebra; 1 Extremal Elements in Lie Algebras; 2 Geometry from Extremal Elements; 3 Root Filtration Spaces; 4 Parapolar Spaces; 5 Degenerate Root Filtration Spaces; 6 Conclusion; References
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Properties of a 27-Dimensional Space of Symmetric Bilinear Forms Acted on by E61 Introduction; 2 Octonion Algebras; 3 The Exceptional 27-Dimensional Jordan Algebra and the Group E6; 4 Subspaces with Special Rank Properties; References; On the Geometry of Global Function Fields, the Riemann-Roch Theorem, and Finiteness Properties of S-Arithmetic Groups; 1 Introduction; 2 Projective Varieties; 3 Curves Over Finite Fields Considered as Varieties; 4 Geometry of Numbers; 5 Curves Over Finite Fields Considered as Schemes; 6 Reduction Theory for Rationally Trivial Group Schemes
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7 Reduction Theory for Reductive Groups Over the Adèles8 Filtrations of Euclidean Buildings; 9 Applications and Conjectures; 9.1 Finiteness Properties of S-Arithmetic Groups; 9.2 Isoperimetric Properties of S-Arithmetic Groups; References; Some Remarks on Two-Transitive Permutation Groupsas Multiplication Groups of Quasigroups; 1 Introduction; 2 Permutation Groups; 3 A Sufficient Condition; 4 Two-Transitive Groups; 4.1 The Almost Simple Two-Transitive Groups; 4.2 The Two-Transitive Groups with Elementary Abelian Socle; 5 Searching for Quasigroups By Computer; References
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Curve Complexes Versus Tits Buildings: Structuresand Applications1 Introduction; 1.1 Summary; 1.2 The Origin of Tits Buildings; 1.3 The Origin of Curve Complexes; 2 Definition of Buildings; 2.1 A Geometric Definition of Tits Buildings via Symmetric Spaces; 2.2 Axioms for Spherical Buildings via Apartments; 2.3 Euclidean and Hyperbolic Buildings; 2.4 Rational Tits Buildings of Linear Algebraic Groups; 3 Definition of Curve Complexes; 4 Geometric and Topological Properties of Buildings; 5 Geometric and Topological Properties of Curve Complexes; 6 Selected Applications of Buildings
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6.1 Automorphism Groups of Buildings6.2 Mostow Strong Rigidity and Generalizations; 6.3 Compactifications of Locally Symmetric Spaces; 6.4 Cohomological Dimension and Duality Properties of Arithmetic Groups; 6.5 Simplicial Volumes of Locally Symmetric Spaces; 6.6 Asymptotic Cones of Symmetric Spaces and Locally Symmetric Spaces; 6.7 Applications of Euclidean Buildings; 6.8 Compactifications of Euclidean Buildings; 7 Applications of Curve Complexes; 7.1 Automorphism Groups of Curve Complexes; 7.2 Isometry Groups of Teichmüller Spaces; 7.3 Ending Lamination Conjecture of Thurston
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7.4 Quasi-Isometric Rigidity of Mapping Class Groups
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Electronic reproduction; Available via World Wide Web
Weitere Ausg.:
ISBN 1283439646
Weitere Ausg.:
ISBN 9781461407089
Sprache:
Englisch
DOI:
10.1007/978-1-4614-0709-6
URL:
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