2011/02/21 by Andries E. Brouwer, Brouwer, Andries E., Mihaela Popoviciu +1
Mathematics · #13A50 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:13A50
paper · pdf · doi:10.48550/arxiv.1102.4250
arxiv created 2011/02/21 · openalex publication_date 2011/02/21 · arxiv updated 2011/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.