On the depth of separating algebras for finite groups

Jonathan Elmer

doi:10.1007/s13366-011-0030-1

On the depth of separating algebras for finite groups

Jonathan Elmer^*

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1007/s13366-011-0030-1
Publication status	Published - Mar 2012

Keywords

Cohomology modules
Depth
Invariant theory
Modular representation theory
Separating algebra

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title = "On the depth of separating algebras for finite groups",

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.",

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author = "Jonathan Elmer",

note = "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. ",

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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.

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KW - Cohomology modules

KW - Depth

KW - Invariant theory

KW - Modular representation theory

KW - Separating algebra

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JF - Beiträge zur Algebra und Geometrie

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On the depth of separating algebras for finite groups

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