
Journal of Lie Theory 25 (2015), No. 2, 485506 Copyright Heldermann Verlag 2015 On a Geometry Associated with Free PseudoProduct Fundamental Graded Lie Algebras Tomoaki Yatsui 192 Masakae, Otaru 0470003, Japan yatsui@frontier.hokudai.ac.jp We calculate the prolongations of the underlying fundamental graded Lie algebras of free pseudoproduct fundamental graded Lie algebras. Also we show that the Lie algebra of infinitesimal automorphisms of a differential system associated with the HilbertCartan equation in a wider sense is isomorphic to the prolongation of the underlying fundamental graded Lie algebra of some free pseudoproduct fundamental graded Lie algebra. Keywords: Pseudoproduct graded Lie algebra, prolongation, HilbertCartan equation. MSC: 17B70; 58A15 [ Fulltextpdf (359 KB)] for subscribers only. 