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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Topological groups. --- Groups, Topological --- Continuous groups

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Property (T) is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property (T) plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property (T): the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property (T).

Topological Groups --- Mathematics --- Topological groups. --- Mathematics. --- Math --- Science --- Groups, Topological --- Continuous groups --- Topological groups --- Kazhdan, D.

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512.546 --- Topological groups --- Groups, Topological --- Continuous groups --- 512.546 Topological groups --- Topological groups. Lie groups --- Groupes topologiques --- Topologische groepen

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Singularities (Mathematics) --- Geometry, Algebraic. --- Topological groups. --- Algebraic geometry --- Geometry --- Groups, Topological --- Continuous groups --- Geometry, Algebraic --- Topological groups --- Singularitats (Matemàtica)

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Groupes et algèbres de Lie, Chapitre 9 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce neuvième chapitre du Livre sur les Groupes et algèbres de Lie, neuvième Livre du traité, comprend les paragraphes : §1 Algèbres de Lie compactes ; §2 Tores maximaux des groupes de Lie compacts ; §3 Fromes compactes des algèbres de Lie semi-simples complexes ; §4 Système de racines associé à un groupe compact ; §5 Classes de conjugaison ; §6 Intégration dans les groupes de Lie compacts ; §7 Représentations irréductibles des groupes de Lie compacts connexes ; §8 Transformation de Fourier ; §9 Opération des groupes de Lie compacts sur les variétés. Ce volume a été publié en 1982.

Lie groups. --- Lie algebras. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Topological Groups. --- Topological Groups, Lie Groups. --- Groups, Topological --- Continuous groups --- Topological groups.