By D. J. H. Garling
Clifford algebras, outfitted up from quadratic areas, have purposes in lots of parts of arithmetic, as normal generalizations of advanced 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. additionally they have their position in physics, atmosphere the scene for Maxwell's equations in electromagnetic concept, for the spin of basic debris and for the Dirac equation. this easy advent to Clifford algebras makes the mandatory algebraic history - together with multilinear algebra, quadratic areas and finite-dimensional actual algebras - simply obtainable 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 quite a few contexts.
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