Invariants of Triangular Lie Algebras

Details Invariants of Triangular Lie Algebras Invariants of Triangular Lie Algebras

2007-04-06

arxiv.org/abs/0704.0937v4

J. Phys. A 40 (2007) 7557-7572

Physics

Mathematical Physics

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

Scientific paper

10.1088/1751-8113/40/27/009

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.

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