caa a22 4500 44586236X CHVBK 20180317145447.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00031-011-9138-5 doi (NATIONALLICENCE)springer-10.1007/s00031-011-9138-5 SL2-modules of small homological dimension [Elektronische Daten] [Andries Brouwer, Mihaela Popoviciu] Let V n be the SL2-module of binary forms of degree n and let $ V = {V_{{n_1}}} \oplus \cdots \oplus {V_{{n_p}}} $ . We consider the algebra $ R = \mathcal{O}{(V)^{{\text{S}}{{\text{L}}_2}}} $ 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 hd R. Popov gave in 1983 a classification of the cases in which hd R ≤ 10 for a single binary form (p = 1) or hd R ≤ 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 hd R ≤ 100, and for p > 1 those with hd R ≤ 15. In these cases we give a set of homogeneous parameters and a set of generators for the algebra R. Springer Science+Business Media, LLC, 2011 Brouwer Andries Department of Mathematics, Eindhoven University of Technology, P. O. Box513, 5600MB, Eindhoven, Netherlands aut Popoviciu Mihaela Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051, Basel, Switzerland aut Transformation Groups SP Birkhäuser Verlag Boston 16/3(2011-09-01), 599-617 1083-4362 16:3<599 2011 16 31 https://doi.org/10.1007/s00031-011-9138-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9138-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brouwer Andries Department of Mathematics, Eindhoven University of Technology, P. O. Box513, 5600MB, Eindhoven, Netherlands aut NATIONALLICENCE 700 1- Popoviciu Mihaela Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051, Basel, Switzerland aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/3(2011-09-01), 599-617 1083-4362 16:3<599 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer