All solvable extensions of a class of nilpotent Lie algebras of dimension<i>n</i>and degree of nilpotency<i>n</i>− 1
Libor ŠnoblFaculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Prague 1, Czech RepublicP. WinternitzCentre de recherches mathématiques and Departement de mathématiques et de statistique, Université de Montréal, CP 6128, Succ Centre-Ville, Montréal, Québec, H3C 3J7, Canada
2009en
ABI
Abstract
We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.
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