Invariants of Triangular Lie Algebras with One Nilindependent Diagonal Element

Details Invariants of Triangular Lie Algebras with One Nilindependent Diagonal Element Invariants of Triangular Lie Algebras with One Nilindependent Diagonal Element

2007-05-16

arxiv.org/abs/0705.2394v3

J. Phys. A 40 (2007), 9783-9792

Physics

Mathematical Physics

LaTeX2e, 10 pages; misprints are corrected, some proofs are extended

Scientific paper

10.1088/1751-8113/40/32/005

The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan's method of moving frames and the special technique developed for for triangular and closed algebras in [J. Phys. A: Math. Theor., 2007, V.40, 7557]. The conjecture of Tremblay and Winternitz [J. Phys. A: Math. Gen., 2001, V.34, 9085] on the number and form of elements in the bases is completed and proved.

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