Diagonal subgroup

The subgroup of a Cartesian power of a given group consisting of all elements with identical components. For instance, the diagonal group of the product is the group of pairs , .

Comments

The phrase diagonal group (or diagonal subgroup) is also used for the subgroup scheme of over a field whose points with values in a -algebra are the diagonal invertible matrices with coefficients in .

Let be a commutative group. The functor from commutative rings with unit element to groups then defines a group scheme. Here is the group of invertible elements of and is the category of groups. Group schemes isomorphic to such group schemes are called diagonizable group schemes.

References

[a1]	M. Demazure, P. Gabriel, "Groupes algébriques" , 1 , North-Holland (1970)