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Lie Groups Their Discrete Subgroups And Invariant Theory
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Book Synopsis Lie Groups, Their Discrete Subgroups, and Invariant Theory by : Ėrnest Borisovich Vinberg
Download or read book Lie Groups, Their Discrete Subgroups, and Invariant Theory written by Ėrnest Borisovich Vinberg and published by American Mathematical Society(RI). This book was released on 1992 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past thirty years, E B Vinberg and L A Onishchik have conducted a seminar on Lie groups at Moscow University; about five years ago V L Popov became the third co-director, and the range of topics expanded to include invariant theory. Today, the seminar encompasses such areas as algebraic groups, geometry and topology of homogeneous spaces, and Kac-Moody groups and algebras. This collection presents a snapshot of the research activities of this well-established seminar, including new results in Lie groups, crystallographic groups, and algebraic transformation groups. These papers will not be published elsewhere. Readers will find this volume useful for the new results it contains as well as for the open problems it poses.
Book Synopsis Discrete Subgroups of Lie Groups by : Madabusi S. Raghunathan
Download or read book Discrete Subgroups of Lie Groups written by Madabusi S. Raghunathan and published by Springer. This book was released on 2012-11-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originated from a course of lectures given at Yale University during 1968-69 and a more elaborate one, the next year, at the Tata Institute of Fundamental Research. Its aim is to present a detailed ac count of some of the recent work on the geometric aspects of the theory of discrete subgroups of Lie groups. Our interest, by and large, is in a special class of discrete subgroups of Lie groups, viz., lattices (by a lattice in a locally compact group G, we mean a discrete subgroup H such that the homogeneous space GJ H carries a finite G-invariant measure). It is assumed that the reader has considerable familiarity with Lie groups and algebraic groups. However most of the results used frequently in the book are summarised in "Preliminaries"; this chapter, it is hoped, will be useful as a reference. We now briefly outline the contents of the book. Chapter I deals with results of a general nature on lattices in locally compact groups. The second chapter is an account of the fairly complete study of lattices in nilpotent Lie groups carried out by Ma1cev. Chapters III and IV are devoted to lattices in solvable Lie groups; most of the theorems here are due to Mostow. In Chapter V we prove a density theorem due to Borel: this is the first important result on lattices in semisimple Lie groups.
Book Synopsis Lie Groups and Invariant Theory by : Ėrnest Borisovich Vinberg
Download or read book Lie Groups and Invariant Theory written by Ėrnest Borisovich Vinberg and published by American Mathematical Soc.. This book was released on 2005 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, devoted to the 70th birthday of A. L. Onishchik, contains a collection of articles by participants in the Moscow Seminar on Lie Groups and Invariant Theory headed by E. B. Vinberg and A. L. Onishchik. The book is suitable for graduate students and researchers interested in Lie groups and related topics.
Book Synopsis Discrete Subgroups of Lie Groups by : M. S. Raghunathan
Download or read book Discrete Subgroups of Lie Groups written by M. S. Raghunathan and published by Springer. This book was released on 1972 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie Groups and Lie Algebras II by : A.L. Onishchik
Download or read book Lie Groups and Lie Algebras II written by A.L. Onishchik and published by Boom Koninklijke Uitgevers. This book was released on 2000-02-03 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic survey of all the basic results on the theory of discrete subgroups of Lie groups, presented in a convenient form for users. The book makes the theory accessible to a wide audience, and will be a standard reference for many years to come.
Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian Hall
Download or read book Lie Groups, Lie Algebras, and Representations written by Brian Hall and published by Springer. This book was released on 2015-05-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette
Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
Book Synopsis Discrete Subgroups of Semisimple Lie Groups by : Gregori Aleksandrovitsch Margulis
Download or read book Discrete Subgroups of Semisimple Lie Groups written by Gregori Aleksandrovitsch Margulis and published by Springer. This book was released on 1991 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Lie Theory of Connected Pro-Lie Groups by : Karl Heinrich Hofmann
Download or read book The Lie Theory of Connected Pro-Lie Groups written by Karl Heinrich Hofmann and published by European Mathematical Society. This book was released on 2007 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonne quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of pro-Lie groups irrespective of local compactness. This study fits very well into the current trend which addresses infinite-dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite-dimensional real Lie algebras to an astonishing degree, even though it has had to overcome greater technical obstacles. This book exposes a Lie theory of connected pro-Lie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finite-dimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis, and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics.
Book Synopsis Topics in Quantum Groups and Finite-Type Invariants by : Boris L. Feigin
Download or read book Topics in Quantum Groups and Finite-Type Invariants written by Boris L. Feigin and published by American Mathematical Soc.. This book was released on 1998 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the first collection of articles consisting entirely of work by the faculty and students at the Higher Mathematics College at the Independent University of Moscow. The 11 contributions cover symmetry groups of regular polyhedra over finite fields, vector bundles on an elliptical curve and Skylanin algebras, Tutte decomposition for graphs and symmetric matrices, and invarians and homology of spaces of knots in arbitrary manifolds. The focus of the text is on quantum groups and low-dimensional topology. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
Book Synopsis Lie Groups, Lie Algebras, and Some of Their Applications by : Robert Gilmore
Download or read book Lie Groups, Lie Algebras, and Some of Their Applications written by Robert Gilmore and published by Courier Corporation. This book was released on 2012-05-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
Book Synopsis Dynamics of Discrete Group Action by : Boris N. Apanasov
Download or read book Dynamics of Discrete Group Action written by Boris N. Apanasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-22 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics – from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.
Book Synopsis Differential Topology, Infinite-Dimensional Lie Algebras, and Applications by : Alexander Astashkevich
Download or read book Differential Topology, Infinite-Dimensional Lie Algebras, and Applications written by Alexander Astashkevich and published by American Mathematical Soc.. This book was released on 1999 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs, and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics.
Book Synopsis Unconventional Lie Algebras by : D. B. Fuks
Download or read book Unconventional Lie Algebras written by D. B. Fuks and published by American Mathematical Soc.. This book was released on 1993 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Equations and Spectral Theory by : M. S. Birman
Download or read book Nonlinear Equations and Spectral Theory written by M. S. Birman and published by American Mathematical Soc.. This book was released on 2007 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translations of articles on mathematics appearing in various Russian mathematical serials.
Book Synopsis Kirillov's Seminar on Representation Theory by : Grigori I. Olshanskiĭ
Download or read book Kirillov's Seminar on Representation Theory written by Grigori I. Olshanskiĭ and published by American Mathematical Soc.. This book was released on 1998 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in Singularity Theory by : Alekseĭ Nikolaevich Khovanskiĭ
Download or read book Topics in Singularity Theory written by Alekseĭ Nikolaevich Khovanskiĭ and published by American Mathematical Soc.. This book was released on 1997 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
