Invariants of triangular Lie algebras with one nilindependent diagonal element

Abstract

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 triangular and related algebras in [J. Phys. A: Math. Theor. 40 (2007), 7557-7572]. The conjecture of Tremblay and Winternitz [J. Phys. A: Math. Gen. 34 (2001), 9085-9099] on the number and form of elements in the bases is completed and proved.

11 pages; enhanced version

References in corpus (7)

• 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
• Invariants of Lie Algebras with Fixed Structure of Nilradicals
• Invariants of the nilpotent and solvable triangular Lie algebras
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Cited by in corpus (2)

• All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
• Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements