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Paper detail

SL2-modules of small homological dimension

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&#39;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.

preprint2011arXivOpen access
Andries E. BrouwerMihaela Popoviciu
math.RT
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Andries E. BrouwerMihaela Popoviciu

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