Introduction To Octonion And Other Non Associative Algebras In Physics
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Author |
: Susumu Okubo |
Publisher |
: Cambridge University Press |
Total Pages |
: 152 |
Release |
: 1995-08-03 |
ISBN-10 |
: 9780521472159 |
ISBN-13 |
: 0521472156 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Introduction to Octonion and Other Non-Associative Algebras in Physics by : Susumu Okubo
In this book, the author aims to familiarize researchers and graduate students in both physics and mathematics with the application of non-associative algebras in physics.Topics covered by the author range from algebras of observables in quantum mechanics, angular momentum and octonions, division algebra, triple-linear products and YangSHBaxter equations. The author also covers non-associative gauge theoretic reformulation of Einstein's general relativity theory and so on. Much of the material found in this book is not available in other standard works.
Author |
: Tevian Dray |
Publisher |
: World Scientific |
Total Pages |
: 229 |
Release |
: 2015 |
ISBN-10 |
: 9789814401821 |
ISBN-13 |
: 981440182X |
Rating |
: 4/5 (21 Downloads) |
Synopsis The Geometry of the Octonions by : Tevian Dray
There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. In addition, more sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics including the remarkable fact that classical supersymmetry only exists in particular spacetime dimensions.Contents: Introduction"Number Systems: "The Geometry of the Complex NumbersThe Geometry of the QuaternionsThe Geometry of the OctonionsOther Number Systems"Symmetry Groups: "Some Orthogonal GroupsSome Unitary GroupsSome Symplectic GroupsSymmetry Groups over Other Division AlgebrasLie Groups and Lie AlgebrasThe Exceptional Groups"Applications: "Division Algebras in MathematicsOctonionic Eigenvalue ProblemsThe Physics of the OctonionsMagic Squares Readership: Advanced ubdergraduate and graduate students and faculty in mathematics and physics; non-experts with moderately sophisticated mathematics background. Key Features: This book is easily digestible by a large audience wanting to know the elementary introduction to octanionsSuitable for any reader with a grasp of the complex numbers, although familiarity with non-octonionic versions of some of the other topics would be helpfulMany open problems are very accessibleAdvanced topics covered are quite sophisticated, leading up to a clear discussion of (one representation of) the exceptional Lie algebras and their associated root diagrams, and of the octonionic projective spaces on which they act
Author |
: Jaak Lõhmus |
Publisher |
: |
Total Pages |
: 296 |
Release |
: 1994 |
ISBN-10 |
: UOM:39015054011534 |
ISBN-13 |
: |
Rating |
: 4/5 (34 Downloads) |
Synopsis Nonassociative Algebras in Physics by : Jaak Lõhmus
Author |
: Lev Sabinin |
Publisher |
: CRC Press |
Total Pages |
: 553 |
Release |
: 2006-01-13 |
ISBN-10 |
: 9781420003451 |
ISBN-13 |
: 1420003453 |
Rating |
: 4/5 (51 Downloads) |
Synopsis Non-Associative Algebra and Its Applications by : Lev Sabinin
With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences.
Author |
: Lev Sabinin |
Publisher |
: CRC Press |
Total Pages |
: 558 |
Release |
: 2006-01-13 |
ISBN-10 |
: 0824726693 |
ISBN-13 |
: 9780824726690 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Non-Associative Algebra and Its Applications by : Lev Sabinin
With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.
Author |
: Dmitri Rabounski |
Publisher |
: Infinite Study |
Total Pages |
: 94 |
Release |
: |
ISBN-10 |
: |
ISBN-13 |
: |
Rating |
: 4/5 ( Downloads) |
Synopsis Progress in Physics, vol. 1/2016 by : Dmitri Rabounski
The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics
Author |
: Cheikh Thiécoumbe Gueye |
Publisher |
: Springer |
Total Pages |
: 254 |
Release |
: 2016-11-21 |
ISBN-10 |
: 9783319329024 |
ISBN-13 |
: 3319329022 |
Rating |
: 4/5 (24 Downloads) |
Synopsis Non-Associative and Non-Commutative Algebra and Operator Theory by : Cheikh Thiécoumbe Gueye
Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he has served as a mentor to a generation of mathematicians in Senegal and around the world.
Author |
: Miguel Cabrera García |
Publisher |
: Cambridge University Press |
Total Pages |
: 759 |
Release |
: 2018-04-12 |
ISBN-10 |
: 9781107043114 |
ISBN-13 |
: 1107043115 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Non-Associative Normed Algebras by : Miguel Cabrera García
The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.
Author |
: Miguel Cabrera García |
Publisher |
: Cambridge University Press |
Total Pages |
: 759 |
Release |
: 2018-04-12 |
ISBN-10 |
: 9781108570763 |
ISBN-13 |
: 1108570763 |
Rating |
: 4/5 (63 Downloads) |
Synopsis Non-Associative Normed Algebras: Volume 2, Representation Theory and the Zel'manov Approach by : Miguel Cabrera García
This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.
Author |
: Tevian Dray |
Publisher |
: World Scientific |
Total Pages |
: 229 |
Release |
: 2015-04-08 |
ISBN-10 |
: 9789814401838 |
ISBN-13 |
: 9814401838 |
Rating |
: 4/5 (38 Downloads) |
Synopsis The Geometry Of The Octonions by : Tevian Dray
There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. In addition, more sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics including the remarkable fact that classical supersymmetry only exists in particular spacetime dimensions.