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Additional
classical group
English Wikipedia - The Free Encyclopedia
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Classical group
In
mathematics
, the
classical groups
are defined as the
special linear groups
over the reals , the
complex numbers
and the
quaternions
together with special
automorphism groups
of
symmetric
or
skew-symmetric
bilinear forms
and
Hermitian
or
skew-Hermitian
sesquilinear forms
defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the
complex classical Lie groups
are four infinite families of
Lie groups
that together with the
exceptional groups
exhaust the classification of
simple Lie groups
. The
compact classical groups
are
compact real forms
of the complex classical groups. The finite analogues of the classical groups are the
classical
groups of Lie type
. The term "classical group" was coined by
Hermann Weyl
, it being the title of his 1939 monograph
The Classical Groups
.
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