Clifford Algebras And Spin Representations Of Orthogonal Groups
DOWNLOAD
Download Clifford Algebras And Spin Representations Of Orthogonal Groups PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Clifford Algebras And Spin Representations Of Orthogonal Groups book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Clifford Algebras And Spin Representations Of Orthogonal Groups
DOWNLOAD
Author : Janice Elizabeth Griffiths
language : en
Publisher:
Release Date : 1976
Clifford Algebras And Spin Representations Of Orthogonal Groups written by Janice Elizabeth Griffiths and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
The Algebraic Theory Of Spinors And Clifford Algebras
DOWNLOAD
Author : Claude Chevalley
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-12-13
The Algebraic Theory Of Spinors And Clifford Algebras written by Claude Chevalley 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 1996-12-13 with Mathematics categories.
In 1982, Claude Chevalley expressed three specific wishes with respect to the publication of his Works. First, he stated very clearly that such a publication should include his non technical papers. His reasons for that were two-fold. One reason was his life long commitment to epistemology and to politics, which made him strongly opposed to the view otherwise currently held that mathematics involves only half of a man. As he wrote to G. C. Rota on November 29th, 1982: "An important number of papers published by me are not of a mathematical nature. Some have epistemological features which might explain their presence in an edition of collected papers of a mathematician, but quite a number of them are concerned with theoretical politics ( . . . ) they reflect an aspect of myself the omission of which would, I think, give a wrong idea of my lines of thinking". On the other hand, Chevalley thought that the Collected Works of a mathematician ought to be read not only by other mathematicians, but also by historians of science.
Clifford Algebras And Lie Theory
DOWNLOAD
Author : Eckhard Meinrenken
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-28
Clifford Algebras And Lie Theory written by Eckhard Meinrenken 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 2013-02-28 with Mathematics categories.
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.
Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications
DOWNLOAD
Author : Alexey P Isaev
language : en
Publisher: World Scientific
Release Date : 2020-07-16
Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications written by Alexey P Isaev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-16 with Science categories.
This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.
Spin Geometry And Orthogonal Groups
DOWNLOAD
Author : David Jaramillo Duque
language : en
Publisher:
Release Date : 2017
Spin Geometry And Orthogonal Groups written by David Jaramillo Duque and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
"In this work, we study Clifford algebras, motivated by the very geometrical problem of finding non-vanishing vector fields over the sphere. The study of such algebras naturally leads to Spin groups which are proven to be the universal covering of the orthogonal groups. We classify Clifford algebras and describe their relation to Spin groups. Studying the irreducible representations of Clifford algebras we get interesting isomorphisms for low dimensional Spin groups. And, at the very end, with the machinery developed we study the construction of non-vanishing vector fields over the sphere and the projective space." -- Tomado del Formato de Documento de Grado.
An Introduction To Clifford Algebras And Spinors
DOWNLOAD
Author : Jayme Vaz Jr.
language : en
Publisher: Oxford University Press
Release Date : 2016
An Introduction To Clifford Algebras And Spinors written by Jayme Vaz Jr. and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
Spinors Clifford And Cayley Algebras
DOWNLOAD
Author : Robert Hermann
language : en
Publisher: Math-Sci Press
Release Date : 1974
Spinors Clifford And Cayley Algebras written by Robert Hermann and has been published by Math-Sci Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Orthogonal And Symplectic Clifford Algebras
DOWNLOAD
Author : A. Crumeyrolle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Orthogonal And Symplectic Clifford Algebras written by A. Crumeyrolle 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 2013-06-29 with Science categories.
The Algebraic Theory Of Spinors
DOWNLOAD
Author : Claude Chevalley
language : en
Publisher:
Release Date : 1954
The Algebraic Theory Of Spinors written by Claude Chevalley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Mathematics categories.
Clifford Algebras And Their Applications In Mathematical Physics
DOWNLOAD
Author : A. Micali
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Clifford Algebras And Their Applications In Mathematical Physics written by A. Micali 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 2013-03-09 with Mathematics categories.
This volume contains selected papers presented at the Second Workshop on Clifford Algebras and their Applications in Mathematical Physics. These papers range from various algebraic and analytic aspects of Clifford algebras to applications in, for example, gauge fields, relativity theory, supersymmetry and supergravity, and condensed phase physics. Included is a biography and list of publications of Mário Schenberg, who, next to Marcel Riesz, has made valuable contributions to these topics. This volume will be of interest to mathematicians working in the fields of algebra, geometry or special functions, to physicists working on quantum mechanics or supersymmetry, and to historians of mathematical physics.