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