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TitleResolutions of 2 and 3 dimensional rings of invariants for cyclic groups.
Author(s) John Harrison, David L. Wehlau
TypeArticle in Journal
AbstractLet G be the cyclic group of order n, and suppose F is a field containing a primitive nth root of unity. We consider the ring of invariants F[W] G of a three dimensional representation W of G where G ⊂ SL(W). We describe minimal generators and relations for this ring and prove that the lead terms of the relations are quadratic. These minimal generators for the relations form a Gröbner basis with a surprisingly simple combinatorial structure. We describe the graded Betti numbers for a minimal free resolution of F[W] G . The case where W is any two dimensional representation of G is also handled.
Keywords Betti numbers, Cyclic group, Gröbner bases, Invariant theory, Minimal resolutions, Monomial ideals, 13A50, 13D02
ISSN0092-7872; 1532-4125/e
URL http://www.tandfonline.com/doi/abs/10.1080/00927872.2012.695834
JournalCommun. Algebra
PublisherTaylor & Francis, Philadelphia, PA
Translation No
Refereed No