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Author : I. Stewart
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (634 download)
Download or read book Structure Theorems for a Class of Locally Finite Lie Algebras written by I. Stewart and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Karl Heinrich Hofmann
Publisher : European Mathematical Society
ISBN 13 : 9783037190326
Total Pages : 704 pages
Book Rating : 4.1/5 (93 download)
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.
Author : Johanna Hennig
Publisher :
ISBN 13 : 9781321870565
Total Pages : 88 pages
Book Rating : 4.8/5 (75 download)
Download or read book Locally Finite Dimensional Lie Algebras written by Johanna Hennig and published by . This book was released on 2015 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, [asterisk]), K(R, [asterisk])]/(Z(R) [intersection] [K(R, [asterisk]), K(R,[asterisk])]) for a simple, locally finite dimensional associative algebra R with involution [asterisk]. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(n[infinity]), o(n[infinity]), and sp(n[infinity]).
Author : David Charles Hobby
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.:/5 (44 download)
Download or read book The Structure of Finite Algebras written by David Charles Hobby and published by . This book was released on 1988 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The utility of congruence lattices in revealing the structure of general algebras has been recognized since Garrett Birkhoff's pioneering work in the 1930s and 1940s. However, the results presented in this book are of very recent origin: most of them were developed in 1983. The main discovery presented here is that the lattice of congruences of a finite algebra is deeply connected to the structure of that algebra. The theory reveals a sharp division of locally finite varieties of algebras into six interesting new families, each of which is characterized by the behavior of congruences in the algebras. The authors use the theory to derive many new results that will be of interest not only to universal algebraists, but to other algebraists as well. The authors begin with a straightforward and complete development of basic tame congruence theory, a topic that offers great promise for a wide variety of investigations. They then move beyond the consideration of individual algebras to a study of locally finite varieties. A list of open problems closes the work.
Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)
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: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author : Helmut Strade
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311051544X
Total Pages : 550 pages
Book Rating : 4.1/5 (15 download)
Download or read book Structure Theory written by Helmut Strade and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-24 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopes Lie algebras of special derivations Derivation simple algebras and modules Simple Lie algebras Recognition theorems The isomorphism problem Structure of simple Lie algebras Pairings of induced modules Toral rank 1 Lie algebras
Author : David L. Armacost
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.:/5 (44 download)
Download or read book The Structure of Locally Compact Abelian Groups written by David L. Armacost and published by . This book was released on 1981 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Antonio Fernández López
Publisher : American Mathematical Soc.
ISBN 13 : 1470450860
Total Pages : 314 pages
Book Rating : 4.4/5 (74 download)
Download or read book Jordan Structures in Lie Algebras written by Antonio Fernández López and published by American Mathematical Soc.. This book was released on 2019-08-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores applications of Jordan theory to the theory of Lie algebras. After presenting the general theory of nonassociative algebras and of Lie algebras, the book then explains how properties of the Jordan algebra attached to a Jordan element of a Lie algebra can be used to reveal properties of the Lie algebra itself.
Author : Ralph McKenzie
Publisher : Springer Science & Business Media
ISBN 13 : 1461245524
Total Pages : 209 pages
Book Rating : 4.4/5 (612 download)
Download or read book Structure of Decidable Locally Finite Varieties written by Ralph McKenzie and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically precise definition of the intuitive notion of "algorithm" was implicit in Kurt Godel's [1931] paper on formally undecidable propo sitions of arithmetic. During the 1930s, in the work of such mathemati cians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godel's idea evolved into the concept of a recursive function. Church pro posed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)-i. e. , that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930). The de termination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A.
Author : Peter Webb
Publisher : Cambridge University Press
ISBN 13 : 1107162394
Total Pages : 339 pages
Book Rating : 4.1/5 (71 download)
Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Author : Nina Stumme
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (594 download)
Download or read book The Structure of Locally Finite Split Lie Algebras written by Nina Stumme and published by . This book was released on 1999 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9400903650
Total Pages : 743 pages
Book Rating : 4.4/5 (9 download)
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author : Sang-hyun Kim
Publisher : Springer Nature
ISBN 13 : 3030890066
Total Pages : 323 pages
Book Rating : 4.0/5 (38 download)
Download or read book Structure and Regularity of Group Actions on One-Manifolds written by Sang-hyun Kim and published by Springer Nature. This book was released on 2021-11-19 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem, which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds, subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups, chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and the study of mapping class groups. The book will be of interest to researchers in geometric group theory.
Author : Mona Merling
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (143 download)
Download or read book A structure theorem for Plesken Lie algebras over finite fields written by Mona Merling and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ana Agore
Publisher : CRC Press
ISBN 13 : 1351168711
Total Pages : 243 pages
Book Rating : 4.3/5 (511 download)
Download or read book Extending Structures written by Ana Agore and published by CRC Press. This book was released on 2019-08-29 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extending Structures: Fundamentals and Applications treats the extending structures (ES) problem in the context of groups, Lie/Leibniz algebras, associative algebras and Poisson/Jacobi algebras. This concisely written monograph offers the reader an incursion into the extending structures problem which provides a common ground for studying both the extension problem and the factorization problem. Features Provides a unified approach to the extension problem and the factorization problem Introduces the classifying complements problem as a sort of converse of the factorization problem; and in the case of groups it leads to a theoretical formula for computing the number of types of isomorphisms of all groups of finite order that arise from a minimal set of data Describes a way of classifying a certain class of finite Lie/Leibniz/Poisson/Jacobi/associative algebras etc. using flag structures Introduces new (non)abelian cohomological objects for all of the aforementioned categories As an application to the approach used for dealing with the classification part of the ES problem, the Galois groups associated with extensions of Lie algebras and associative algebras are described
Author : Ian Stewart
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.:/5 (41 download)
Download or read book Lie Algebras Generated by Finite-dimensional Ideals written by Ian Stewart and published by Pitman Publishing. This book was released on 1975 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel Gorenstein
Publisher : Springer Science & Business Media
ISBN 13 : 1468484974
Total Pages : 339 pages
Book Rating : 4.4/5 (684 download)
Download or read book Finite Simple Groups written by Daniel Gorenstein and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: In February 1981, the classification of the finite simple groups (Dl)* was completed,t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined efforts of several hundred mathematicians from around the world over a period of 30 years, the full proof covered something between 5,000 and 10,000 journal pages, spread over 300 to 500 individual papers. The single result that, more than any other, opened up the field and foreshadowed the vastness of the full classification proof was the celebrated theorem of Walter Feit and John Thompson in 1962, which stated that every finite group of odd order (D2) is solvable (D3)-a statement expressi ble in a single line, yet its proof required a full 255-page issue of the Pacific 10urnal of Mathematics [93]. Soon thereafter, in 1965, came the first new sporadic simple group in over 100 years, the Zvonimir Janko group 1 , to further stimulate the 1 'To make the book as self-contained as possible. we are including definitions of various terms as they occur in the text. However. in order not to disrupt the continuity of the discussion. we have placed them at the end of the Introduction. We denote these definitions by (DI). (D2), (D3). etc.
