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  3. Clifford Algebras: An Introduction
  • Cited by 46
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 June 2012
      23 June 2011
      ISBN:
      9780511972997
      9781107096387
      9781107422193
      DOI:
      https://doi.org/10.1017/CBO9780511972997
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.45kg, 210 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.29kg, 210 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Algebra
      Series:
      London Mathematical Society Student Texts (78)
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    • Selected: Digital
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    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
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    [ABS] M. F., Atiyah, R., Bott and A., Shapiro, Clifford modules, Topology 3 (Supplement 1) (1964), 3–38.
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    [Por1] I. R., Porteous, Topological Geometry, Cambridge University Press, Cambridge, 1981.
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    [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.
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