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线性代数群[Linear Algebraic Group] [2005-4-19]
iamet 发表在 ∑〖数学〗
| 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. |
学好数理化，走遍天下都不怕！ | |
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