The Structure of Compact Groups

Beschreibung

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.
Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups, on compact Lie groups, and on locally compact abelian groups. However, the thrust of book points in the direction of the structure theory of infinite dimensional, not necessarily commutative compact groups, unfettered by weight restrictions or dimensional bounds. In the process it utilizes infinite dimensional Lie algebras and the exponential function of arbitrary compact groups. The first edition of 1998 was well received by reviewers and has been frequently quoted in the areas of instruction and research. For the present new edition the text has been cleaned of typographical flaws and some minor inaccuracies of content; it has been edited and improved in various sections. New material has been added in order to reflect ongoing research. In the process of revising the original edition, the integrity of the original section numbering was carefully respected so that citations of material from the first edition remains perfectly viable to the users of this edition.

Autor*in

Karl H. Hofmann

Themen in »The Structure of Compact Groups«

Abelian group Lie algebra category theory compact group topological group. Kompakte Gruppe Abelsche Gruppe Topologische Gruppe Kategorientheorie Lie-Algebra

Stimmen zu »The Structure of Compact Groups«

"Thus, the book is informative and carefully written; the exposition is fresh and excellent. It can be useful for students as well as for experts and will meet, as well as the first edition, a wide audience."Victor Gichev in: Zentralblatt MATH 17/2008
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