### Abstract

In this paper we present an algorithm for determining whether a subgroup

*H*of a non-connected reductive group*G*is*G*-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, such as checking whether a certain subgroup of*G**is*^{0}*G**-cr. This essentially reduces the problem of determining*^{0}*G*-complete reducibility to the connected case.Original language | English |
---|---|

Pages (from-to) | 1085-1100 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 3 |

Early online date | 12 Nov 2014 |

DOIs | |

Publication status | Published - Mar 2015 |

### Fingerprint

### Keywords

- G -complete reducibility
- non- connected reductive groups

### Cite this

Bate, M., Herpel, S., Martin, B., & Rohrle, G. (2015).

*G*-complete reducibility in non-connected groups.*Proceedings of the American Mathematical Society*,*143*(3), 1085-1100. https://doi.org/10.1090/S0002-9939-2014-12348-3