The Other Classical Groups
Special linear group (or projective group) over a division algebra DK over K.
(a) Hermitian (i.e., “special” unitary) group for a hermitian form over a quadratic extension K’ of K. (b) Id. for a non-commutative central division algebra DK’ over K’, with an involution inducing on K’ the non-trivial automorphism of K’ over K.
Orthogonal group for a quadratic form over K.
Antihermitian group for an antihermitian (or “skewhermitian”) form over a quaternion algebra over K, with its usual involution.
Symplectic group over K.
Hermitian group for a hermitian form over a quaternion algebra over K, with its usual involution.
KeywordsDivision Algebra Finite Measure Quadratic Extension Quaternion Algebra Affine Space
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