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The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.
List of contents
Chapter 1. A classification of Curtis-Tits amalgams.- Chapter 2. The use of valuations for classifying point-line geometries.- Chapter 3. An outline of polar spaces: basics and advances.- Chapter 4. Embeddings of Line-grassmannians of Polar Spaces in Grassmann Varieties.- Chapter 5. Generation of Lie Incidence Geometries: A Survey.- Chapter 6. Witt-Type Theorems for Subspaces of Lie Geometries: A Survey.- Chapter 7. Embeddings of cotriangular spaces.- Chapter 8. Unipotent Overgroups in Simple Algebraic Groups.- Chapter 9. The axes of a Majorana representation of A12.- Chapter 10. GIT related problems of the flag variety for the action of a maximal torus.- Chapter 11. Characterizations of trialities of type Iid in buildings of type D4.- Chapter 12. On the isomorphism problem for Coxeter groups and related topics.- Chapter 13. Lectures on Artin groups and the K(pi; 1) conjecture. Chapter 14. Algebraic codes and geometry of some classical generalized polygons.- Chapter 15. Some Weyl modules of the algebraic groups of type E_6.- Problem Set.
About the author
N.S. NARASIMHA SASTRY is Professor and Head of Department of Mathematics at Indian Statistical Institute, Bengaluru, India. He received his Ph.D. from University of Pittsburgh, Pennsylvania, USA and has held visiting positions at Tata Institute of Fundamental Research, Mumbai, India; Michigan State University, East Lansing, USA; University of Western Australia, Perth, Australia; Rutgers University, New Brunswick, USA; University of Florida, Gainsville, USA and University of Ghent, Belgium. He has served as referee for journals such as Journal of Algebra; Codes, Designs and Cryptography and Journal of Pure and Applied Algebra and has published in journals such as Journal of Algebra, Journal of Combinatorial Theory (Series A), Geometriae Dedicata, Journal of Functional Analysis, Journal of Operator Theory, Proceedings in Indian Academy of Sciences, Journal of Algebraic Combinatorics and Archiv der Mathematik. Some of the books edited by him include Groups, Finite Geometries and Buildings, published by Springer and Essays in Geometric Group Theory, published by the Ramanujam Mathematical Society. He has co-edited Perspectives in Mathematical Sciences, (Volumes 1 and 2), published by World Scientific. His research interests are finite groups including finite simple groups, geometries related to finite simple groups, algebraic codes, Coxeter groups and the Monster.
Summary
The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.
