Classical Groups and Geometric Algebra
Jan 2002 · Fields Institute Communications Ibhuku elingu-39 · American Mathematical Soc.
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Classical groups, named so by Hermann Weyl, are groups of matrices or quotients of matrix groups by small normal subgroups. Thus the story begins, as Weyl suggested, with the general linear group GLULn(V) of all invertible linear transformations of a vector space V over a field F. All further groups discussed are either subgroups of GLULn(V) or closely related quotient groups. Most of the classical groups consist of invertible linear transformations that respect a bilinear form having some geometric significance, for example, a quadratic form, a symplectic form, and so forth.
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