### Abstract

Consider a finite group G acting on a vector space V over a field K of characteristic p > 0. A separating algebra is a subalgebra A of the ring of invariants K[V]
^{G} with the same point separation properties. In this article we compare the depth of an arbitrary separating algebra with that of the corresponding ring of invariants. We show that, in some special cases, the depth of A is bounded above by the depth of K[V]
^{G}.

Original language | English |
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Pages (from-to) | 31-39 |

Number of pages | 9 |

Journal | Beiträge zur Algebra und Geometrie |

Volume | 53 |

Issue number | 1 |

Early online date | 11 May 2011 |

DOIs | |

Publication status | Published - Mar 2012 |

### Keywords

- Cohomology modules
- Depth
- Invariant theory
- Modular representation theory
- Separating algebra

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## Cite this

Elmer, J. (2012). On the depth of separating algebras for finite groups.

*Beiträge zur Algebra und Geometrie*,*53*(1), 31-39. https://doi.org/10.1007/s13366-011-0030-1