## Abstract

We study solvability, nilpotency and splitting property for algebraic supergroups over an arbitrary field K of characteristic charK≠2. Our first main theorem tells us that an algebraic supergroup G is solvable if the associated algebraic group G_{ev} is trigonalizable. To prove it we determine the algebraic supergroups G such that dimLie(G)_{1}=1; their representations are studied when G_{ev} is diagonalizable. The second main theorem characterizes nilpotent connected algebraic supergroups. A super-analogue of the Chevalley Decomposition Theorem is proved, though it must be in a weak form. An appendix is given to characterize smooth Noetherian superalgebras as well as smooth Hopf superalgebras.

Original language | English |
---|---|

Pages (from-to) | 339-365 |

Number of pages | 27 |

Journal | Journal of Pure and Applied Algebra |

Volume | 221 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1 2017 |

Externally published | Yes |

## ASJC Scopus subject areas

- Algebra and Number Theory