By D. J. H. Garling
Clifford algebras, outfitted up from quadratic areas, have purposes in lots of parts of arithmetic, as ordinary 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 remodel. additionally they have their position in physics, atmosphere the scene for Maxwell's equations in electromagnetic idea, for the spin of common 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 actual algebras - simply obtainable to analyze scholars and final-year undergraduates. the writer additionally introduces many functions in arithmetic and physics, equipping the reader with Clifford algebras as a operating device in various contexts.
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