Semisimple algebraic group
- 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 connected, normal, abelian subgroups.
Examples
* Every direct sum of simple algebraic groups is semisimple.
Properties
References
* | year=1991 | volume=126
* | year=1972
* | year=1998 | volume=9
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