Non-separability and complete reducibility: $E_n$ examples with an application to a question of K\"ulshammer

Tomohiro Uchiyama

Non-separability and complete reducibility: $E_n$ examples with an application to a question of K\"ulshammer

Group Theory 2017-01-31 v4

Authors: Tomohiro Uchiyama

Abstract

Let $G$ be a simple algebraic group of type $E_n (n=6,7,8)$ defined over an algebraically closed field $k$ of characteristic $2$ . We present examples of triples of closed reductive groups $H<M<G$ such that $H$ is $G$ -completely reducible, but not $M$ -completely reducible. As an application, we consider a question of K\"ulshammer on representations of finite groups in reductive groups. We also consider a rationality problem for $G$ -complete reducibility and a problem concerning conjugacy classes.

Keywords

simple algebraic group complete reducibility non-separability type E_n reductive subgroup Külshammer question conjugacy class

Cite

@article{arxiv.1510.00997,
  title  = {Non-separability and complete reducibility: $E_n$ examples with an application to a question of K\"ulshammer},
  author = {Tomohiro Uchiyama},
  journal= {arXiv preprint arXiv:1510.00997},
  year   = {2017}
}

Comments

To appear in J. Group Theory. arXiv admin note: text overlap with arXiv:1309.3807

Non-separability and complete reducibility: $E_n$ examples with an application to a question of K\"ulshammer

Abstract

Keywords

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