A user friendly proof of Nagata's characterization of linearly reductive groups in positive characteristics

作者：Kohls Martin^*

来源：Linear and Multilinear Algebra, 2011, 59(3): 271-278.

DOI：10.1080/03081080903402939

• algebraic groups
• linearly reductive groups
• invariant theory

Let K be an algebraically closed field of positive characteristic p, and G be a linear algebraic group over K. We give a user friendly proof of Nagata's theorem that every finite-dimensional rational representation of G is completely reducible if and only if the connected component G(0) is a torus and p does not divide the index (G: G(0)).

• 出版日期2011