All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

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.

arXiv comment19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be published

References in corpus (12)

• A class of solvable Lie algebras and their Casimir Invariants
• Computation of Invariants of Lie Algebras by Means of Moving Frames
• Solvable Lie algebras with triangular nilradicals
• Solvable Lie algebras with naturally graded nilradicals and their invariants
• Invariants of solvable rigid Lie algebras up to dimension 8
• Invariants of Lie Algebras with Fixed Structure of Nilradicals
• Invariants of the nilpotent and solvable triangular Lie algebras
• Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements
• On the invariants of some solvable rigid Lie algebras
• Determinantal formulae for the Casimir operators of inhomogeneous Lie algebras
• Invariants of Triangular Lie Algebras
• Invariants of triangular Lie algebras with one nilindependent diagonal element

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• Invariants of Lie algebras via moving frames
• Spectral invariants for finite dimensional Lie algebras
• Foliations formed by generic coadjoint orbits of a class of 7-dimensional real solvable Lie groups
• Nilpotent Decomposition of Solvable Lie Algebras
• Residually solvable extensions of an infinite dimensional filiform Leibniz algebra