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semisimple algebraic group
In mathematics, especially in the areas of abstract algebra and algebraic geometry studying linear algebraic groups, a semisimple algebraic group is a type of matrix group which behaves much like a semisimple Lie algebra or semisimple ring.
== Definition ==
A linear algebraic group is called semisimple if and only if the (solvable) radical of the identity component is trivial.
Equivalently, a semisimple linear algebraic group has no non-trivial connected, normal, abelian subgroups.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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