Introduction To Octonion And Other Non Associative Algebras In Physics
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Introduction To Octonion And Other Non Associative Algebras In Physics
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Author : Susumu Okubo
language : en
Publisher: Cambridge University Press
Release Date : 1995-08-03
Introduction To Octonion And Other Non Associative Algebras In Physics written by Susumu Okubo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-03 with Mathematics categories.
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.
Non Associative Algebra And Its Applications
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Author : Lev Sabinin
language : en
Publisher: CRC Press
Release Date : 2006-01-13
Non Associative Algebra And Its Applications written by Lev Sabinin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-13 with Mathematics categories.
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.
Non Associative And Non Commutative Algebra And Operator Theory
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Author : Cheikh Thiécoumbe Gueye
language : en
Publisher: Springer
Release Date : 2016-11-21
Non Associative And Non Commutative Algebra And Operator Theory written by Cheikh Thiécoumbe Gueye and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-21 with Mathematics categories.
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.
Progress In Physics Vol 1 2016
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Author : Dmitri Rabounski
language : en
Publisher: Infinite Study
Release Date :
Progress In Physics Vol 1 2016 written by Dmitri Rabounski and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics
Non Associative Normed Algebras
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Author : Miguel Cabrera García
language : en
Publisher: Cambridge University Press
Release Date : 2018-04-12
Non Associative Normed Algebras written by Miguel Cabrera García and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-12 with Mathematics categories.
The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.
The Geometry Of The Octonions
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Author : Tevian Dray
language : en
Publisher: World Scientific
Release Date : 2015-04-08
The Geometry Of The Octonions written by Tevian Dray and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-08 with Mathematics categories.
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.
Clifford Algebras And Their Applications In Mathematical Physics
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Author : Rafał Abłamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Clifford Algebras And Their Applications In Mathematical Physics written by Rafał Abłamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.
Clifford Algebras And Their Applications In Mathematical Physics
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Author : Rafal Ablamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Clifford Algebras And Their Applications In Mathematical Physics written by Rafal Ablamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
Algebra And Applications 1
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Author : Abdenacer Makhlouf
language : en
Publisher: John Wiley & Sons
Release Date : 2021-03-12
Algebra And Applications 1 written by Abdenacer Makhlouf and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-12 with Mathematics categories.
This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.
Algebra Geometry And Mathematical Physics
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Author : Abdenacer Makhlouf
language : en
Publisher: Springer
Release Date : 2014-06-17
Algebra Geometry And Mathematical Physics written by Abdenacer Makhlouf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-17 with Mathematics categories.
This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers and advanced students.