By D. J. H. Garling
Clifford algebras, equipped up from quadratic areas, have purposes in lots of parts of arithmetic, as typical generalizations of complicated numbers and the quaternions. they're famously utilized in proofs of the Atiyah-Singer index theorem, to supply double covers (spin teams) of the classical teams and to generalize the Hilbert rework. in addition they have their position in physics, environment the scene for Maxwell's equations in electromagnetic conception, for the spin of uncomplicated debris and for the Dirac equation. this simple creation to Clifford algebras makes the required algebraic historical past - together with multilinear algebra, quadratic areas and finite-dimensional genuine algebras - simply available to investigate scholars and final-year undergraduates. the writer additionally introduces many purposes in arithmetic and physics, equipping the reader with Clifford algebras as a operating instrument in a number of contexts.
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