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With every quadratic space φ over a field K one can associate in a functorial way a K-algebra C(φ) called the Clifford algebra of φ. This construction is of fundamental importance in the algebraic theory of quadratic forms. In particular, the invariants e, d, c introduced in chapter 2 find a natural interpretation here. Many properties of these invariants are obvious in the context of Clifford algebras. Moreover, it is easy to include the case of characteristic 2.
KeywordsNormal Form Quadratic Form Clifford Algebra Universal Property Orthogonal Group
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