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  1. Home
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  3. Clifford Algebras: An Introduction
  • Cited by 35
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2011
Online ISBN:
9780511972997
DOI:
https://doi.org/10.1017/CBO9780511972997
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Algebra
Series:
London Mathematical Society Student Texts (78)
Information

Book description

Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah–Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.

Reviews

'… it became clear that Garling has spotted a need for a particular type of book, and has delivered it extremely well. Of all the books written on the subject, Garling's is by some way the most compact and concise … this is a very good book which provides a balanced and concise introduction to the subject of Clifford algebras. Math students will find it ideal for quickly covering a range of algebraic properties, and physicists will find it a very handy source of reference for a variety of material.'

Chris Doran Source: SIAM News

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Contents

Contents
References
References
References
[Art] E., Artin, Geometric algebra, John Wiley, New York, 1988.
[ABS] M. F., Atiyah, R., Bott and A., Shapiro, Clifford modules, Topology 3 (Supplement 1) (1964), 3–38.
[AtS] M. F., Atiyah and I. M., Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963), 422–433.
[Bay] William E., Baylis (editor), Clifford (Geometric) Algebras, Birkhäuser, New York, 1996.
[BGV] Nicole, Berline, Ezra Getzler and Michèle Vergne, Heat Kernels and Dirac Operators, Springer, Berlin, 1996.
[BDS] F., Brackx, R., Delanghe and F., Sommen, Clifford Analysis, Pitman, London, 1983.
[BtD] Theodor, Bröcker and Tammo tom, Dieck, Representations of Compact Lie groups, Springer, Berlin, 1995.
[Che] Claude, Chevalley, The Algebraic Theory of Spinors and Clifford Algebras, Collected works, Volume 2, Springer, Berlin, 1997.
[Cli1] W. K., Clifford, Applications of Grassmann's extensive algebra, Amer. J. Math. 1 (1876) 350–358.
[Cli2] W. K., Clifford, On the classification of geometric algebras, Mathematical papers, William Kingdon Clifford, AMS Chelsea Publishing, 2007, 397–401.
[Coh] P. M., Cohn, Classic Algebra, John Wiley, Chichester, 2000.
[Dir] P. A. M., Dirac, The Principles of Quantum Mechanics, Fourth Edition, Oxford University Press, 1958
[DoL] Chris, Doran and Anthony, Lasenby, Geometric Algebra for Physicists, Cambridge University Press, Cambridge, 2003.
[Duo] Javier, Duoandikoetxea, Fourier Analysis, Amer. Math. Soc., Providence, RI, 2001.
[GRF] J., Garcia-Cuerva and J. L., Rubio de Francia, Weighted Norm Inequalities and Related Topics, North Holland, Amsterdam, 1985.
[GiM] John E., Gilbert and Margaret M. E., Murray, Clifford Algebras and Dirac Operators in Harmonic Analysis, Cambridge University Press, Cambridge, 1991.
[Hah] Alexander J., Hahn, Quadratic Algebras, Clifford Algebras and Arithmetic Witt Groups, Springer, Berlin, 1994.
[Har] F., Reese Harvey, Spinors and Calibrations, Academic Press, San Diego, CA, 1990.
[HeM] Jacques, Helmstetter and Artibano, Micali, Quadratic Mappings and Clifford Algebras, Birkhaüser, Basel, 2008.
[Jac] Nathan, Jacobson, Basic Algebra I and II, W.H. Freeman, San Francisco, CA, 1974, 1980
[Lam] T. Y., Lam, Introduction to Quadratic Forms over Fields, Amer. Math. Soc., Providence, RI, 2004.
[Lan] E. C., LanceHilbert C*-modules, London Mathematical Society Lecture notes 210, Cambridge University Press, Cambridge, 1995.
[LaM] H., Blaine Lawson Jr., and Marie-Louise, Michelsohn, Spin Geometry, Princeton University Press, Princeton, NJ, 1989.
[Lou] Pertti, Lounesto, Clifford Algebras and Spinors, London Mathematical Society Lecture notes 286, Cambridge University Press, Cambridge, 2001.
[MaB] Saunders Mac, Lane and Garrett, Birkhoff, Algebra Third Edition, AMS Chelsea, 1999.
[Mey] Paul-André, Meyer, Quantum Probability for Probabilists, Springer Lecture Notes in Mathematics 1538, Springer, Berlin, 1993.
[PeR] R., Penrose and W., Rindler, Spinors and Space-time I and II, Cambridge University Press, Cambridge, 1984, 1986.
[P1R] R. J., Plymen and P. L., Robinson, Spinors in Hilbert Space, Cambridge University Press, Cambridge, 1994.
[Por1] I. R., Porteous, Topological Geometry, Cambridge University Press, Cambridge, 1981.
[Por2] I. R., Porteous, Clifford Algebras and the Classical Groups, Cambridge University Press, Cambridge, 1995.
[Roe] John, Roe, Elliptic Operators, Topology and Asymptotic Methods, Second edition, Chapman and Hall/CRC, London 2001.
[Rya] John, Ryan (editor), Clifford Algebras in Analysis and Related Topics, CRC Press, Boca Raton, FL, 1996.
[Sep] Mark R., Sepanski, Compact Lie Groups, Springer, Berlin, 2007.
[Ste] Elias M., Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970.
[StW] Elias M., Stein and Guido, Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, NJ, 1971.
[Sud] Anthony, Sudbery, Quantum Mechanics and the Particles of Nature, Cambridge University Press, Cambridge, 1986.

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