### Abstract

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

Pages (from-to) | 1053-1062 |

Number of pages | 10 |

Journal | Quarterly Journal of Mathematics |

Volume | 69 |

Issue number | 3 |

Early online date | 16 Mar 2018 |

DOIs | |

Publication status | Published - 30 Sep 2018 |

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### Keywords

- Invariant theory
- coinvariants
- prime characteristic

### Cite this

*Quarterly Journal of Mathematics*,

*69*(3), 1053-1062. https://doi.org/10.1093/qmath/hay013

**Locally finite derivations and modular coinvariants.** / Elmer, Jonathan; Sezer, Müfit (Corresponding Author).

Research output: Contribution to journal › Article

*Quarterly Journal of Mathematics*, vol. 69, no. 3, pp. 1053-1062. https://doi.org/10.1093/qmath/hay013

}

TY - JOUR

T1 - Locally finite derivations and modular coinvariants

AU - Elmer, Jonathan

AU - Sezer, Müfit

N1 - The second author (M.S.) is supported by a grant from TUBITAK:114F427

PY - 2018/9/30

Y1 - 2018/9/30

N2 - We consider a finite dimensional $\kk G$-module V of a p-group G over a field $\kk$ of characteristic p. We describe a generating set for the corresponding Hilbert Ideal. In case G is cyclic this yields that the algebra $\kk[V]_G$ of coinvariants is a free module over its subalgebra generated by $\kk G$-module generators of V∗. This subalgebra is a quotient of a polynomial ring by pure powers of its variables. The coinvariant ring was known to have this property only when G was cyclic of prime order, \cite{SezerCoinv}. In addition, we show that if G is the Klein 4-group and V does not contain an indecomposable summand isomorphic to the regular module, then the Hilbert Ideal is a complete intersection, extending a result of the second author and R. J. Shank \cite{SezerShank}.

AB - We consider a finite dimensional $\kk G$-module V of a p-group G over a field $\kk$ of characteristic p. We describe a generating set for the corresponding Hilbert Ideal. In case G is cyclic this yields that the algebra $\kk[V]_G$ of coinvariants is a free module over its subalgebra generated by $\kk G$-module generators of V∗. This subalgebra is a quotient of a polynomial ring by pure powers of its variables. The coinvariant ring was known to have this property only when G was cyclic of prime order, \cite{SezerCoinv}. In addition, we show that if G is the Klein 4-group and V does not contain an indecomposable summand isomorphic to the regular module, then the Hilbert Ideal is a complete intersection, extending a result of the second author and R. J. Shank \cite{SezerShank}.

KW - Invariant theory

KW - coinvariants

KW - prime characteristic

U2 - 10.1093/qmath/hay013

DO - 10.1093/qmath/hay013

M3 - Article

VL - 69

SP - 1053

EP - 1062

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 3

ER -