## Abstract

Let p be an odd prime and let G be a non-abelian finite p-group of exponent p
^{2}
with three distinct characteristic subgroups, namely 1, G
^{p}
and G. The quotient group G/G
^{p}
gives rise to an anti-commutative
_{p}
-algebra L such that the action of Aut (L) is irreducible on L; we call such an algebra IAC. This paper establishes a duality G â†" L between such groups and such IAC algebras. We prove that IAC algebras are semisimple and we classify the simple IAC algebras of dimension at most 4 over certain fields. We also give other examples of simple IAC algebras, including a family related to the m-th symmetric power of the natural module of SL(2, ).

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

Pages (from-to) | 1827-1852 |

Number of pages | 26 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 150 |

Issue number | 4 |

Early online date | 25 Feb 2019 |

DOIs | |

Publication status | Published - 1 Aug 2020 |