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Topological groups. Lie groups --- 512.812 --- Lie groups --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- General Lie group theory. Properties, structure, generalizations. Lie groups and Lie algebras --- Lie groups. --- 512.812 General Lie group theory. Properties, structure, generalizations. Lie groups and Lie algebras --- Lie, Groupes de --- Représentations de groupes de Lie

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The representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G. Kac. This book begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine Lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations.

Infinite dimensional Lie algebras. --- Lie algebras. --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Lie algebras --- Infinite dimensional Lie algebras --- 512.812 --- 517.986.5 --- 517.986.5 Infinite-dimensional representations of Lie algebras --- Infinite-dimensional representations of Lie algebras --- 512.812 General Lie group theory. Properties, structure, generalizations. Lie groups and Lie algebras --- General Lie group theory. Properties, structure, generalizations. Lie groups and Lie algebras --- Algèbres de Lie de dimension infinie --- Algèbres de Lie

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This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms.

Forms, Quadratic. --- Algebra. --- Mathematics --- Mathematical analysis --- Quadratic forms --- Diophantine analysis --- Forms, Binary --- Number theory --- Algebra over a field. --- Algebraic group. --- Associative property. --- Axiom. --- Classical group. --- Clifford algebra. --- Commutator. --- Defective matrix. --- Division algebra. --- Fiber bundle. --- Geometry. --- Isotropic quadratic form. --- Jacques Tits. --- Jordan algebra. --- Moufang. --- Non-associative algebra. --- Polygon. --- Precalculus. --- Projective plane. --- Quadratic form. --- Simple Lie group. --- Subgroup. --- Theorem. --- Vector space.

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Following the tremendous reception of our first volume on topological groups called ""Topological Groups: Yesterday, Today, and Tomorrow"", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

coarse structure --- descriptive set theory --- group representation --- thick set --- free topological group --- character --- selectively sequentially pseudocompact --- separable topological group --- quotient group --- Chabauty topology --- pseudo-?-bounded --- topological group --- free precompact Boolean group --- right-angled Artin groups --- Neretin’s group --- coarse space --- ultrafilter space --- endomorphism --- separable --- absolutely closed topological group --- tree --- strongly pseudocompact --- Gromov’s compactification --- dynamical system --- semigroup compactification --- tame function --- compact topological semigroup --- vast set --- space of closed subgroups --- reflexive group --- Lie group --- matrix coefficient --- maximal ideal --- topological semigroup --- ballean --- continuous inverse algebra --- extension --- subgroup --- Thompson’s group --- scale --- isomorphic embedding --- arrow ultrafilter --- H-space --- paratopological group --- pseudocompact --- Ramsey ultrafilter --- fibre bundle --- locally compact group --- product --- large set in a group --- Vietoris topology --- topological group of compact exponent --- Bourbaki uniformity --- p-compact --- mapping cylinder --- syndetic set --- p-adic Lie group --- Boolean topological group --- non-trivial convergent sequence --- fixed point algebra --- polish group topologies --- varieties of coarse spaces --- piecewise syndetic set --- maximal space

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Following the tremendous reception of our first volume on topological groups called ""Topological Groups: Yesterday, Today, and Tomorrow"", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

coarse structure --- descriptive set theory --- group representation --- thick set --- free topological group --- character --- selectively sequentially pseudocompact --- separable topological group --- quotient group --- Chabauty topology --- pseudo-?-bounded --- topological group --- free precompact Boolean group --- right-angled Artin groups --- Neretin’s group --- coarse space --- ultrafilter space --- endomorphism --- separable --- absolutely closed topological group --- tree --- strongly pseudocompact --- Gromov’s compactification --- dynamical system --- semigroup compactification --- tame function --- compact topological semigroup --- vast set --- space of closed subgroups --- reflexive group --- Lie group --- matrix coefficient --- maximal ideal --- topological semigroup --- ballean --- continuous inverse algebra --- extension --- subgroup --- Thompson’s group --- scale --- isomorphic embedding --- arrow ultrafilter --- H-space --- paratopological group --- pseudocompact --- Ramsey ultrafilter --- fibre bundle --- locally compact group --- product --- large set in a group --- Vietoris topology --- topological group of compact exponent --- Bourbaki uniformity --- p-compact --- mapping cylinder --- syndetic set --- p-adic Lie group --- Boolean topological group --- non-trivial convergent sequence --- fixed point algebra --- polish group topologies --- varieties of coarse spaces --- piecewise syndetic set --- maximal space