Resolutions of 2 and 3 Dimensional Rings of Invariants for Cyclic Groups |
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Authors: | John C. Harris |
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Affiliation: | Department of Mathematics and Natural Sciences , D'Youville College , Buffalo , New York , USA |
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Abstract: | Let 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. |
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Keywords: | Betti numbers Cyclic group Gröbner bases Invariant theory Minimal resolutions Monomial ideals |
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