Invariants of Triangular Lie Algebras

Abstract

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], developed further in [J. Phys. A: Math. Theor., 2007, V.40, 113; math-ph/0606045], is used to determine the invariants. A conjecture of [J. Phys. A: Math. Gen., 2001, V.34, 9085], concerning the number of independent invariants and their form, is corroborated.

LaTeX2e, 16 pages; misprints are corrected, some proofs are extended

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• Solvable Lie algebras with triangular nilradicals
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Cited by in corpus (4)

• 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
• Invariants of triangular Lie algebras with one nilindependent diagonal element
• Invariants of Lie algebras via moving frames