A user friendly proof of Nagata's characterization of linearly reductive groups in positive characteristics |
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| Authors: | Martin Kohls |
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| Institution: | 1. Zentrum Mathematik – M11, Technische Universit?t München , Boltzmannstrasse 3, 85748 Garching, Germany kohls@ma.tum.de |
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| Abstract: | 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). |
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| Keywords: | algebraic groups linearly reductive groups invariant theory |
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