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On Graded Lie Like Algebras
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Book Synopsis Geometry of Lie Groups by : B. Rosenfeld
Download or read book Geometry of Lie Groups written by B. Rosenfeld and published by Springer Science & Business Media. This book was released on 1997-02-28 with total page 424 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.
Book Synopsis Lie Algebras Graded by the Root Systems BC$_r$, $r\geq 2$ by : Bruce Normansell Allison
Download or read book Lie Algebras Graded by the Root Systems BC$_r$, $r\geq 2$ written by Bruce Normansell Allison and published by American Mathematical Soc.. This book was released on 2002 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra, $r\ge 3$ (excluding type $\mathrm{D}_3)$ Models for $\mathrm{BC}_r$-graded Lie algebras, $r\ge 3$ (excluding type $\mathrm{D}_3)$ The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Central extensions, derivations and invariant forms Models of $\mathrm{BC}_r$-graded Lie algebras with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Appendix: Peirce decompositions in structurable algebras References.
Book Synopsis Introduction to Finite and Infinite Dimensional Lie (Super)algebras by : Neelacanta Sthanumoorthy
Download or read book Introduction to Finite and Infinite Dimensional Lie (Super)algebras written by Neelacanta Sthanumoorthy and published by Academic Press. This book was released on 2016-04-26 with total page 514 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. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. - Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory - Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities - Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras - Focuses on Kac-Moody algebras
Book Synopsis Lie Algebras and Applications by : Francesco Iachello
Download or read book Lie Algebras and Applications written by Francesco Iachello and published by Springer. This book was released on 2007-02-22 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
Book Synopsis Gradings on Simple Lie Algebras by : Alberto Elduque
Download or read book Gradings on Simple Lie Algebras written by Alberto Elduque and published by American Mathematical Soc.. This book was released on 2013 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some non-classical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form.
Book Synopsis Lie Algebras and Their Representations by : Seok-Jin Kang
Download or read book Lie Algebras and Their Representations written by Seok-Jin Kang and published by American Mathematical Soc.. This book was released on 1996 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
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 Modular Lie Algebras and their Representations by : H. Strade
Download or read book Modular Lie Algebras and their Representations written by H. Strade and published by CRC Press. This book was released on 2020-08-11 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.
Book Synopsis Abstract Lie Algebras by : David J. Winter
Download or read book Abstract Lie Algebras written by David J. Winter and published by Courier Corporation. This book was released on 2008-01-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972 edition.
Book Synopsis Abstract Lie Algebras by : David J Winter
Download or read book Abstract Lie Algebras written by David J Winter and published by Courier Corporation. This book was released on 2013-12-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.
Book Synopsis On graded Lie-like algebras by : Andrzej Krzysztof Kwaśniewski
Download or read book On graded Lie-like algebras written by Andrzej Krzysztof Kwaśniewski and published by . This book was released on 1989 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie Algebras of Finite and Affine Type by : Roger William Carter
Download or read book Lie Algebras of Finite and Affine Type written by Roger William Carter and published by Cambridge University Press. This book was released on 2005-10-27 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Book Synopsis The Recognition Theorem for Graded Lie Algebras in Prime Characteristic by : Georgia Benkart
Download or read book The Recognition Theorem for Graded Lie Algebras in Prime Characteristic written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 2009 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 197, number 920 (second of 5 numbers)."
Book Synopsis Lie Algebras In Particle Physics by : Howard Georgi
Download or read book Lie Algebras In Particle Physics written by Howard Georgi and published by Westview Press. This book was released on 1999-10-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exciting new edition of a classic text
Book Synopsis Clifford Algebras and Lie Theory by : Eckhard Meinrenken
Download or read book Clifford Algebras and Lie Theory written by Eckhard Meinrenken and published by Springer Science & Business Media. This book was released on 2013-02-28 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.
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: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Book Synopsis Graded Lie Algebras in Mathematics and Physics by : Philip A. Vetter
Download or read book Graded Lie Algebras in Mathematics and Physics written by Philip A. Vetter and published by . This book was released on 1990 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
