### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Beiträge zur Algebra und Geometrie*,

*53*(1), 31-39. https://doi.org/10.1007/s13366-011-0030-1

**On the depth of separating algebras for finite groups.** / Elmer, Jonathan.

Research output: Contribution to journal › Article

*Beiträge zur Algebra und Geometrie*, vol. 53, no. 1, pp. 31-39. https://doi.org/10.1007/s13366-011-0030-1

}

TY - JOUR

T1 - On the depth of separating algebras for finite groups

AU - Elmer, Jonathan

N1 - Acknowledgments This work was completed during a short stay at RWTH-Aachen. The author would like to thank Julia Hartmann for making this stay possible. Special thanks go to Martin Kohls for Example 5.1 and various useful MAGMA routines, and to an anonymous referee for a couple of helpful suggestions.

PY - 2012/3

Y1 - 2012/3

N2 - 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.

AB - 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.

KW - Cohomology modules

KW - Depth

KW - Invariant theory

KW - Modular representation theory

KW - Separating algebra

UR - http://www.scopus.com/inward/record.url?scp=84856877043&partnerID=8YFLogxK

U2 - 10.1007/s13366-011-0030-1

DO - 10.1007/s13366-011-0030-1

M3 - Article

AN - SCOPUS:84856877043

VL - 53

SP - 31

EP - 39

JO - Beiträge zur Algebra und Geometrie

JF - Beiträge zur Algebra und Geometrie

SN - 0138-4821

IS - 1

ER -