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.
Articles by others on the same topic
There are currently no matching articles.