= Linearly reductive algebraic group
An <affine algebraic group> is linearly reductive when every finite-dimensional <rational representation> is completely reducible. Equivalently its invariants functor is exact. Over a field of characteristic zero, <reductive algebraic groups> are linearly reductive; in positive characteristic this stronger property fails for many reductive groups. An <algebraic torus> is linearly reductive in every characteristic because its rational representations decompose into character spaces.
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