Invariants of triangular Lie algebras with one nilindependent diagonal element

2007/05/31 by Vyacheslav Boyko, Jiri Patera, Roman O. Popovych · 2 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.RT #msc:17B05 #msc:17B10 #msc:17B30 #msc:22E70 #msc:58D19 #msc:81R05

paper · pdf · doi:10.1088/1751-8113/40/32/005

published as J. Phys. A 40 (2007), 9783-9792 · 11 pages; enhanced version

arxiv created 2018/04/01 · arxiv updated 2018/04/03

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.

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• Invariants of solvable lie algebras with triangular nilradicals and diagonal nilindependent elements
• Invariants of Lie algebras via moving frames

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