SL2-modules of small homological dimension
Representation Theory
2011-02-22 v1
Abstract
Let Vn be the SL2-module of binary forms of degree n and let V = Vn1+...+Vnp . We consider the algebra R of polynomial functions on V invariant under the action of SL2. The measure of the intricacy of these algebras is the length of their chains of syzygies, called homological dimension hdR. Popov gave in 1983 a classification of the cases in which hdR <=10 for a single binary form (p = 1) or hdR <=3 for a system of two or more binary forms (p > 1). We extend Popov's result and determine for p = 1 the cases with hdR <= 100, and for p > 1 those with hdR <= 15. In these cases we give a set of homogeneous parameters and a set of generators for the algebra R.
Cite
@article{arxiv.1102.4250,
title = {SL2-modules of small homological dimension},
author = {Andries E. Brouwer and Mihaela Popoviciu},
journal= {arXiv preprint arXiv:1102.4250},
year = {2011}
}