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Full Description
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.
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(π; 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.
