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Arithmetic groups --- Linear algebraic groups --- 512.54 --- Algebraic groups, Linear --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- 512.54 Groups. Group theory --- Groups. Group theory

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This book treats Jacques Tits's beautiful theory of buildings, making that theory accessible to readers with minimal background. It includes all the material of the earlier book Buildings by the second-named author, published by Springer-Verlag in 1989, which gave an introduction to buildings from the classical (simplicial) point of view. This new book also includes two other approaches to buildings, which nicely complement the simplicial approach: On the one hand, buildings may be viewed as abstract sets of chambers with a Weyl-group-valued distance function; this point of view has become increasingly important in the theory and applications of buildings. On the other hand, buildings may be viewed as metric spaces. Beginners can still use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher. There are several paths through the book, so that readers may choose to concentrate on one particular approach. The pace is gentle in the elementary parts of the book, and the style is friendly throughout. All concepts are well motivated. There are thorough treatments of advanced topics such as the Moufang property, with arguments that are much more detailed than those that have previously appeared in the literature. This book is suitable as a textbook, with many exercises, and it may also be used for self-study.

Buildings (Group theory) --- Immeubles (Théorie des groupes) --- Buildings (Group theory). --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Linear algebraic groups. --- Immeubles (Théorie des groupes) --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Theory of buildings (Group theory) --- Tits's theory of buildings (Group theory) --- Algebraic groups, Linear --- Mathematics. --- Algebraic geometry. --- Group theory. --- Topological groups. --- Lie groups. --- Group Theory and Generalizations. --- Algebraic Geometry. --- Topological Groups, Lie Groups. --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- Linear algebraic groups --- Geometry, algebraic. --- Topological Groups. --- Groups, Topological --- Continuous groups --- Algebraic geometry --- Geometry --- Groups, Theory of --- Substitutions (Mathematics) --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Geometry, Algebraic.

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D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. Significant concepts and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig conjecture using D-module theory. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, and representation theory.

Ordered algebraic structures --- Geometry --- algebra --- topologie (wiskunde) --- Topological groups. Lie groups --- Algebra --- landmeetkunde --- wiskunde --- Group theory --- Représentations d'algèbres de Lie --- Representations of Lie algebras --- Linear algebraic groups. --- D-modules. --- Representations of groups. --- Groupes algébriques linéaires --- D-modules, Théorie des --- Représentations de groupes --- Groupes algébriques linéaires --- D-modules, Théorie des --- Représentations de groupes

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Algebra --- 51 <082.1> --- Mathematics--Series --- Semisimple Lie groups --- Linear algebraic groups --- Geometric group theory --- Lorentz groups --- Symmetric spaces --- Rings (Algebra) --- Groupes de Lie semi-simples --- Groupes algébriques linéaires --- Groupes, Théorie géométrique des --- Lorentz, Groupes de --- Espaces symétriques --- Anneaux (algèbre) --- Spaces, Symmetric --- Geometry, Differential --- Semi-simple Lie groups --- Lie groups --- Algebraic rings --- Ring theory --- Algebraic fields --- Algebraic groups, Linear --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- Groups, Lorentz --- Continuous groups --- Groupes de Lie semi-simples. --- Groupes algébriques linéaires. --- Groupes, Théorie géométrique des. --- Lorentz, Groupes de. --- Espaces symétriques.