Download or read book Conjugacy Classes in Semisimple Algebraic Groups written by James E. Humphreys and published by American Mathematical Soc.. This book was released on 1995 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.
Download or read book Conjugacy Classes in Algebraic Groups written by R. Steinberg and published by Springer. This book was released on 2006-11-15 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conjugacy Classes in Lie Algebras and Algebraic Groups written by R. W Richardson (Jr) and published by . This book was released on 1966 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kostant has shown that a complex semi-simple Lie algebra has only a finite number of nilpotent conjugacy classes. This paper shows how Kostant's theorem can be obtained as a special case of an elementary theorem on conjugacy classes in reductive subgroups of algebrais subgroups. As a corollary of this theorem we show that a semi-simple algebrais group over an algebraically closed field of characteristic p> 5 has only a finite number of unipotent conjugacy classes. Related conjugacy theorems are proved for subalgebras and homomorphisms of Lie algebras. (Author).
Download or read book Conjugacy Classes of N tuples in Lie Algebras and Algebraic Groups written by R. W. Richardson and published by . This book was released on 1987 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Lie Groups written by B. Rosenfeld and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.
Download or read book Algebraic Groups and Lie Groups written by Gus Lehrer and published by Cambridge University Press. This book was released on 1997-01-23 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains original research articles by many of the world's leading researchers in algebraic and Lie groups. Its inclination is algebraic and geometic, although analytical aspects are included. The central theme reflects the interests of R. W. Richardson, viz connections between representation theory and the structure and geometry of algebraic groups. All workers on algebraic and Lie groups will find that this book contains a wealth of interesting material.
Download or read book Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2012-01-25 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.
Download or read book Finite Groups of Lie Type written by Roger W. Carter and published by . This book was released on 1993-08-24 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite groups of Lie type are of basic importance in the theory of groups. A classic in its field, this book presents the theories of finite groups of Lie type in a clear and accessible style, especially with regard to the main concepts of the theory and the techniques of proof used, and gives a detailed exposition of the complex representation theory.
Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Download or read book Seminar on Algebraic Groups and Related Finite Groups written by Armand Borel and published by Springer. This book was released on 2006-11-14 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Groups and their Representations written by R.W. Carter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.
Download or read book Conjugacy Classes in Algebraic Groups written by Robert Steinberg and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lie Groups and Algebraic Groups written by Arkadij L. Onishchik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.
Download or read book The Markoff and Lagrange Spectra written by Thomas W. Cusick and published by American Mathematical Soc.. This book was released on 1989 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Markoff and Lagrange spectra. The authors have gathered and systemized numerous results from the diverse and scattered literature, much of which has appeared in rather inaccessible Russian publications. Readers will find a comprehensive overview of the theory of the Markoff and Lagrange spectra, starting with the origins of the subject in two papers of A. Markoff from 1879-80. Most of the progress since that time has occurred in the last 20 years or so, when there has been a resurgence of interest in these spectra. The authors provide an excellent exposition of these developments, in addition to presenting many proofs and correcting various errors in the literature.
Download or read book Algebra Carbondale 1980 written by Ralph K. Amayo and published by Springer. This book was released on 2006-11-15 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Lie Algebras and Representation Theory written by J.E. Humphreys and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.
Download or read book Lie Algebras and Algebraic Groups written by Patrice Tauvel and published by Springer Science & Business Media. This book was released on 2005-08-08 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the theory of Lie algebras and algebraic groups, this book includes a large amount of commutative algebra and algebraic geometry so as to make it as self-contained as possible. The aim of the book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included, and some recent results are discussed in the final chapters.
