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Maximal Abelian Subalgebras Of Pseudoeuclidean Real Lie Algebras And Their Application In Physics
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Book Synopsis Maximal Abelian Subalgebras of Pseudoeuclidean Real Lie Algebras and Their Application in Physics by : Zora Thomova
Download or read book Maximal Abelian Subalgebras of Pseudoeuclidean Real Lie Algebras and Their Application in Physics written by Zora Thomova and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie Algebras by : Gerard G. A. Bäuerle
Download or read book Lie Algebras written by Gerard G. A. Bäuerle and published by North Holland. This book was released on 1990 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I. The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras. The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.
Book Synopsis Noncompact Semisimple Lie Algebras and Groups by : Vladimir K. Dobrev
Download or read book Noncompact Semisimple Lie Algebras and Groups written by Vladimir K. Dobrev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-09-12 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory supplemented by many concrete examples for a great variety of noncompact semisimple Lie algebras and groups. Contents: Introduction Lie Algebras and Groups Real Semisimple Lie Algebras Invariant Differential Operators Case of the Anti-de Sitter Group Conformal Case in 4D Kazhdan–Lusztig Polynomials, Subsingular Vectors, and Conditionally Invariant Equations Invariant Differential Operators for Noncompact Lie Algebras Parabolically Related to Conformal Lie Algebras Multilinear Invariant Differential Operators from New Generalized Verma Modules Bibliography Author Index Subject Index
Download or read book Nilpotent Lie Algebras written by M. Goze and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the theory of nilpotent Lie algebras and their applications. Nilpotent Lie algebras have played an important role over the last years both in the domain of algebra, considering its role in the classification problems of Lie algebras, and in the domain of differential geometry. Among the topics discussed here are the following: cohomology theory of Lie algebras, deformations and contractions, the algebraic variety of the laws of Lie algebras, the variety of nilpotent laws, and characteristically nilpotent Lie algebras in nilmanifolds. Audience: This book is intended for graduate students specialising in algebra, differential geometry and in theoretical physics and for researchers in mathematics and in theoretical physics.
Book Synopsis Classical Lie Algebras at Infinity by : Ivan Penkov
Download or read book Classical Lie Algebras at Infinity written by Ivan Penkov and published by Springer Nature. This book was released on 2022-01-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Book Synopsis Infinite-dimensional Lie Algebras by : R.K. Amayo
Download or read book Infinite-dimensional Lie Algebras written by R.K. Amayo and published by Springer. This book was released on 1974-10-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is only in recent times that infinite-dimensional Lie algebras have been the subject of other than sporadic study, with perhaps two exceptions: Cartan's simple algebras of infinite type, and free algebras. However, the last decade has seen a considerable increase of interest in the subject, along two fronts: the topological and the algebraic. The former, which deals largely with algebras of operators on linear spaces, or on manifolds modelled on linear spaces, has been dealt with elsewhere*). The latter, which is the subject of the present volume, exploits the surprising depth of analogy which exists between infinite-dimen sional Lie algebras and infinite groups. This is not to say that the theory consists of groups dressed in Lie-algebraic clothing. One of the tantalising aspects of the analogy, and one which renders it difficult to formalise, is that it extends to theorems better than to proofs. There are several cases where a true theorem about groups translates into a true theorem about Lie algebras, but where the group-theoretic proof uses methods not available for Lie algebras and the Lie-theoretic proof uses methods not available for groups. The two theories tend to differ in fine detail, and extra variations occur in the Lie algebra case according to the underlying field. Occasionally the analogy breaks down altogether. And of course there are parts of the Lie theory with no group-theoretic counterpart.
Book Synopsis Maximal Abelian Subalgebras of Complex Euclidean Lie Algebras by : Ernest Gunter Kalnins
Download or read book Maximal Abelian Subalgebras of Complex Euclidean Lie Algebras written by Ernest Gunter Kalnins and published by . This book was released on 1994 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Infinite-dimensional Lie Algebra by : Minoru Wakimoto
Download or read book Lectures on Infinite-dimensional Lie Algebra written by Minoru Wakimoto and published by World Scientific. This book was released on 2001 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G Kac. This book begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance and are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine Lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations.
Book Synopsis Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises by : Sven Bodo Wirsing
Download or read book Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises written by Sven Bodo Wirsing and published by Anchor Academic Publishing. This book was released on 2017-11-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within series II we extend the theory of maximal nilpotent substructures to solvable associative algebras, especially for their group of units and their associated Lie algebra. We construct all maximal nilpotent Lie subalgebras and characterize them by simple and double centralizer properties. They possess distinctive attractor and repeller characteristics. Their number of isomorphic classes is finite and can be bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are extremal among all maximal nilpotent Lie subalgebras. The maximal nilpotent Lie subalgebras are connected to the maximal nilpotent subgroups. This correspondence is bijective via forming the group of units and creating the linear span. Cartan subalgebras and Carter subgroups as well as the Lie nilradical and the Fitting subgroup are linked by this correspondence. All partners possess the same class of nilpotency based on a theorem of Xiankun Du. By using this correspondence we transfer all results to maximal nilpotent subgroups of the group of units. Carter subgroups and the Fitting subgroup turn out to be extremal among all maximal nilpotent subgroups. All four extremal substructures are proven to be Fischer subgroups, Fischer subalgebras, nilpotent injectors and projectors. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory.
Book Synopsis Lie Algebras, Vertex Operator Algebras and Their Applications by : Yi-Zhi Huang
Download or read book Lie Algebras, Vertex Operator Algebras and Their Applications written by Yi-Zhi Huang and published by American Mathematical Soc.. This book was released on 2007 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.
Book Synopsis Lie Superalgebras and Enveloping Algebras by : Ian Malcolm Musson
Download or read book Lie Superalgebras and Enveloping Algebras written by Ian Malcolm Musson and published by American Mathematical Soc.. This book was released on 2012-04-04 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.
Book Synopsis Dissertation Abstracts International by :
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2000 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Physics A written by and published by . This book was released on 1998 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on fundamental mathematical and computational methods underpinning physics. Relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics, classical and quantum integrable systems and classical and quantum field theory.
Book Synopsis Finite and Infinite Dimensional Lie Algebras and Applications in Physics by : Gerard G. A. Bäuerle
Download or read book Finite and Infinite Dimensional Lie Algebras and Applications in Physics written by Gerard G. A. Bäuerle and published by . This book was released on 1990 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Commutative Subalgebras of Semi-simple Lie Algebras by : Anatoliĭ Ivanovich Malʹt︠s︡ev
Download or read book Commutative Subalgebras of Semi-simple Lie Algebras written by Anatoliĭ Ivanovich Malʹt︠s︡ev and published by . This book was released on 1951 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, by : Niky Kamran
Download or read book Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, written by Niky Kamran and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrodinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.
Download or read book Canadian Journal of Physics written by and published by . This book was released on 1994-07 with total page 1118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
