Journal of Lie Theory 25 (2015), No. 2, 485--506
Copyright Heldermann Verlag 2015
On a Geometry Associated with Free Pseudo-Product Fundamental Graded Lie Algebras
Tomoaki Yatsui
1--9--2 Masakae, Otaru 047-0003, Japan
yatsui@frontier.hokudai.ac.jp
We calculate the prolongations of the underlying fundamental graded Lie algebras of free pseudo-product fundamental graded Lie algebras. Also we show that the Lie algebra of infinitesimal automorphisms of a differential system associated with the Hilbert-Cartan equation in a wider sense is isomorphic to the prolongation of the underlying fundamental graded Lie algebra of some free pseudo-product fundamental graded Lie algebra.
Keywords: Pseudo-product graded Lie algebra, prolongation, Hilbert-Cartan equation.
MSC: 17B70; 58A15
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