Clifford Algebras : an Introduction.

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A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Garling, D. J. H.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2011.
Colección:London Mathematical Society Student Texts, 78.
Temas:
Clifford algebras.
Algèbres de Clifford.
MATHEMATICS > Algebra > Linear.
Álgebras de Clifford
Clifford algebras
Acceso en línea:Texto completo

MARC

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100 1 |a Garling, D. J. H. 
245 1 0 |a Clifford Algebras :  |b an Introduction. 
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490 1 |a London Mathematical Society Student Texts, 78 
505 0 |a Cover; London Mathematical Society Student Texts 78: Clifford Algebras: An Introduction; Title; Copyright; Contents; Introduction; PART ONE: THE ALGEBRAIC ENVIRONMENT; 1: Groups and vector spaces; 1.1 Groups; 1.2 Vector spaces; 1.3 Duality of vector spaces; 2: Algebras, representations and modules; 2.1 Algebras; 2.2 Group representations; 2.3 The quaternions; 2.4 Representations and modules; 2.5 Module homomorphisms; 2.6 Simple modules; 2.7 Semi-simple modules; 3: Multilinear algebra; 3.1 Multilinear mappings; 3.2 Tensor products; 3.3 The trace. 
505 8 |a 3.4 Alternating mappings and the exterior algebra3.5 The symmetric tensor algebra; 3.6 Tensor products of algebras; 3.7 Tensor products of super-algebras; PART TWO: QUADRATIC FORMS AND CLIFFORD ALGEBRAS; 4: Quadratic forms; 4.1 Real quadratic forms; 4.2 Orthogonality; 4.3 Diagonalization; 4.4 Adjoint mappings; 4.5 Isotropy; 4.6 Isometries and the orthogonal group; 4.8 The Cartan-Dieudonné theorem; 4.9 The groups SO(3) and SO(4); 4.10 Complex quadratic forms; 4.11 Complex inner-product spaces; 5: Clifford algebras; 5.1 Clifford algebras; 5.2 Existence; 5.3 Three involutions. 
505 8 |a 5.4 Centralizers, and the centre5.5 Simplicity; 5.6 The trace and quadratic form on A(E, q); 5.7 The group G(E; q) of invertible elements of A(E, q); 6: Classifying Clifford algebras; 6.1 Frobenius' theorem; 6.2 Clifford algebras A(E, q) with dimE = 2; 6.3 Clifford's theorem; 6.4 Classifying even Clifford algebras; 6.5 Cartan's periodicity law; 6.6 Classifying complex Clifford algebras; 7: Representing Clifford algebras; 7.1 Spinors; 7.2 The Clifford algebras Ak, k; 7.3 The algebras Bk, k+1 and Ak, k+1; 7.4 The algebras Ak+1,k and Ak+2,k; 7.5 Clifford algebras A(E, q) with dim E = 3. 
505 8 |a 7.6 Clifford algebras A(E, q) with dim E = 47.7 Clifford algebras A(E, q) with dim E = 5; 7.8 The algebras A6, B7, A7 and A8; 8: Spin; 8.1 Clifford groups; 8.2 Pin and Spin groups; 8.3 Replacing q by?q; 8.4 The spin group for odd dimensions; 8.5 Spin groups, for d = 2; 8.6 Spin groups, for d = 3; 8.7 Spin groups, for d = 4; 8.8 The group Spin5; 8.9 Examples of spin groups for d>= 6; 8.10 Table of results; PART THREE: SOME APPLICATIONS; 9: Some applications to physics; 9.1 Particles with spin 1/2; 9.2 The Dirac operator; 9.3 Maxwell's equations; 9.4 The Dirac equation. 
505 8 |a 10: Clifford analyticity10.1 Clifford analyticity; 10.2 Cauchy's integral formula; 10.3 Poisson kernels and the Dirichlet problem; 10.4 The Hilbert transform; 10.5 Augmented Dirac operators; 10.6 Subharmonicity properties; 10.7 The Riesz transform; 10.8 The Dirac operator on a Riemannian manifold; 11: Representations of Spind and SO(d); 11.1 Compact Lie groups and their representations; 11.2 Representations of SU(2); 11.3 Representations of Spind and SO(d) for d<=4; 12: Some suggestions for further reading; The algebraic environment; Quadratic spaces; Clifford algebras. 
500 |a Clifford algebras and harmonic analysis. 
520 |a A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics. 
588 0 |a Print version record. 
504 |a Includes bibliographical references (pages 191-192) and index. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
650 0 |a Clifford algebras. 
650 6 |a Algèbres de Clifford. 
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650 7 |a Álgebras de Clifford  |2 embne 
650 7 |a Clifford algebras  |2 fast 
776 0 8 |i Print version:  |a Garling, D.J.H.  |t Clifford Algebras : An Introduction.  |d Cambridge : Cambridge University Press, ©2011  |z 9781107096387 
830 0 |a London Mathematical Society Student Texts, 78. 
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