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

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

2008-09-18

arxiv.org/abs/0809.3259v2

J. Phys. A: Math. Theor. 42 (2009) 105201

Physics

Mathematical Physics

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

Scientific paper

10.1088/1751-8113/42/10/105201

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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