By D. J. H. Garling
Clifford algebras, outfitted up from quadratic areas, have purposes in lots of components of arithmetic, as average 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. in addition they have their position in physics, surroundings the scene for Maxwell's equations in electromagnetic thought, for the spin of effortless debris and for the Dirac equation. this easy advent to Clifford algebras makes the mandatory algebraic heritage - together with multilinear algebra, quadratic areas and finite-dimensional genuine algebras - simply available to analyze scholars and final-year undergraduates. the writer additionally introduces many purposes in arithmetic and physics, equipping the reader with Clifford algebras as a operating software in a number of contexts.
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