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2005/04/19 | 线性代数群[Linear Algebraic Group]
类别(∑〖数学〗)
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发表于 13:20
A linear algebraic group is a
matrix group
that is also an
affine variety
. In particular, its elements satisfy polynomial equations. The group operations are required to be given by
regular rational functions
. The linear algebraic groups are similar to the
Lie groups
, except that linear algebraic groups may be defined over any
field
, including those of positive
field characteristic
.
The
special linear group
of matrices of determinant one
is a linear algebraic group. This is because the equation for the
determinant
is a polynomial equation in the entries of the matrices. The
general linear group
of matrices with non-zero determinant
is also a linear algebraic group. This can be seen by introducing an extra variable Y and writing
This is a polynomial equation in
variables and is equivalent to saying that
is nonzero. This equation describes
as an
affine variety
.
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