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| Author | : Gregori A. Margulis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 408 |
| Release | : 1991-02-15 |
| Genre | : Mathematics |
| ISBN | : 9783540121794 |
Download Discrete Subgroups of Semisimple Lie Groups Book in PDF, ePub and Kindle
Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students.
| Author | : M. S. Raghunathan |
| Publisher | : Springer |
| Total Pages | : 250 |
| Release | : 1972 |
| Genre | : Mathematics |
| ISBN | : |
Download Discrete Subgroups of Lie Groups Book in PDF, ePub and Kindle
| Author | : Gregori A. Margulis |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 1991-03-01 |
| Genre | : Mathematics |
| ISBN | : 9783642514456 |
Download Discrete Subgroups of Semisimple Lie Groups Book in PDF, ePub and Kindle
A detailed treatment of the geometric aspects of discrete groups was carried out by Raghunathan in his book "Discrete subgroups of Lie Groups" which appeared in 1972. In particular he covered the theory of lattices in nilpotent and solvable Lie groups, results of Mal'cev and Mostow, and proved the Borel density theorem and local rigidity theorem ofSelberg-Weil. He also included some results on unipotent elements of discrete subgroups as well as on the structure of fundamental domains. The chapters concerning discrete subgroups of semi simple Lie groups are essentially concerned with results which were obtained in the 1960's. The present book is devoted to lattices, i.e. discrete subgroups of finite covolume, in semi-simple Lie groups. By "Lie groups" we not only mean real Lie groups, but also the sets of k-rational points of algebraic groups over local fields k and their direct products. Our results can be applied to the theory of algebraic groups over global fields. For example, we prove what is in some sense the best possible classification of "abstract" homomorphisms of semi-simple algebraic group over global fields.
| Author | : A.L. Onishchik |
| Publisher | : Boom Koninklijke Uitgevers |
| Total Pages | : 238 |
| Release | : 2000-02-03 |
| Genre | : Mathematics |
| ISBN | : 9783540505853 |
Download Lie Groups and Lie Algebras II Book in PDF, ePub and Kindle
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.
| Author | : Armand Borel |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 282 |
| Release | : 2013-11-21 |
| Genre | : Mathematics |
| ISBN | : 147041225X |
Download Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups Book in PDF, ePub and Kindle
It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.
| Author | : Walter L. Baily |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 366 |
| Release | : 1975 |
| Genre | : Mathematics |
| ISBN | : |
Download Discrete Subgroups of Lie Groups and Applications to Moduli Book in PDF, ePub and Kindle
"This book contains the original papers presented at an International Cooloquium on Discrete Subgroups of Lie Groups and Applications to Moduli held at the Tata Institute of Fundamental Research in January 1973" -- Back cover.
| Author | : Brian Hall |
| Publisher | : Springer |
| Total Pages | : 452 |
| Release | : 2015-05-11 |
| Genre | : Mathematics |
| ISBN | : 3319134671 |
Download Lie Groups, Lie Algebras, and Representations Book in PDF, ePub and Kindle
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
| Author | : Gregori Aleksandrovitch Margulis |
| Publisher | : |
| Total Pages | : 388 |
| Release | : 1991 |
| Genre | : |
| ISBN | : |
Download Discrete Subgroups of Semisimple Lie Groups Book in PDF, ePub and Kindle
| Author | : Ėrnest Borisovich Vinberg |
| Publisher | : American Mathematical Society(RI) |
| Total Pages | : 224 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : |
Download Lie Groups, Their Discrete Subgroups, and Invariant Theory Book in PDF, ePub and Kindle
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.
| Author | : J.A. Wolf |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 498 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 940098961X |
Download Harmonic Analysis and Representations of Semisimple Lie Groups Book in PDF, ePub and Kindle
This book presents the text of the lectures which were given at the NATO Advanced Study Institute on Representations of Lie groups and Harmonic Analysis which was held in Liege from September 5 to September 17, 1977. The general aim of this Summer School was to give a coordinated intro duction to the theory of representations of semisimple Lie groups and to non-commutative harmonic analysis on these groups, together with some glance at physical applications and at the related subject of random walks. As will appear to the reader, the order of the papers - which follows relatively closely the order of the lectures which were actually give- follows a logical pattern. The two first papers are introductory: the one by R. Blattner describes in a very progressive way a path going from standard Fourier analysis on IR" to non-commutative harmonic analysis on a locally compact group; the paper by J. Wolf describes the structure of semisimple Lie groups, the finite-dimensional representations of these groups and introduces basic facts about infinite-dimensional unitary representations. Two of the editors want to thank particularly these two lecturers who were very careful to pave the way for the later lectures. Both these chapters give also very useful guidelines to the relevant literature.
