# Complete reducibility and separability

@article{Bate2007CompleteRA, title={Complete reducibility and separability}, author={Michael Bate and Benjamin Martin and Gerhard R{\"o}hrle and Rudolf Tange}, journal={Transactions of the American Mathematical Society}, year={2007}, volume={362}, pages={4283-4311} }

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general theorems concerning G-complete reducibility. We demonstrate that many of these results fail without…

## 48 Citations

### Complete reducibility and commuting subgroups

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Abstract Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p ≧ 0. We study J.-P. Serre's notion of G-complete reducibility for subgroups of G.…

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