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An Introduction to Real Clifford Algebras and Their Classification

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dc.contributor.advisor Singman, David Neilson, Christopher S.
dc.creator Neilson, Christopher S. 2012-07-27 2012-09-17T21:22:28Z NO_RESTRICTION en_US 2012-09-17T21:22:28Z 2012-09-17
dc.description.abstract Real Clifford algebras are associative, unital algebras that arise from a pairing of a finite-dimensional real vector space and an associated nondegenerate quadratic form. Herein, all the necessary mathematical background is provided in order to develop some of the theory of real Clifford algebras. This includes the idea of a universal property, the tensor algebra, the exterior algebra, and Z2-graded algebras. Clifford algebras are defined by means of a universal property and shown to be realizable algebras that are nontrivial. The proof of the latter fact is fairly involved and all details of proof are given. A method for creating a basis of any Clifford algebra is given. We conclude by giving a classification of all real Clifford algebras as various matrix algebras.
dc.language.iso en en_US
dc.subject universal property en_US
dc.subject tensor algebra en_US
dc.subject Clifford algebra en_US
dc.subject exterior algebra en_US
dc.subject multilinear algebra en_US
dc.subject quadratic form en_US
dc.title An Introduction to Real Clifford Algebras and Their Classification en_US
dc.type Thesis en Master of Science in Mathematics en_US Master's en Mathematics en George Mason University en

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