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单词 Reductive
释义

reductive


Let G be a Lie group or algebraic group. G is called reductive over a field k if every representation of G over k is completely reducible

For example, a finite groupMathworldPlanetmath is reductive over a field k if and only if its order is not divisible by the characteristic of k (by Maschke’s theorem). A complex Lie group is reductive if and only if it is a direct productMathworldPlanetmathPlanetmathPlanetmathPlanetmath of a semisimple group and an algebraic torus.

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更新时间:2025/5/4 16:09:28