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 |
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Keywords
- Cohomology modules
- Depth
- Invariant theory
- Modular representation theory
- Separating algebra
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology
Cite this
On the depth of separating algebras for finite groups. / Elmer, Jonathan.
In: Beiträge zur Algebra und Geometrie, Vol. 53, No. 1, 03.2012, p. 31-39.Research output: Contribution to journal › Article
}
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 -