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.
Cite
@article{arxiv.0704.0937,
title = {Invariants of Triangular Lie Algebras},
author = {Vyacheslav Boyko and Jiri Patera and Roman Popovych},
journal= {arXiv preprint arXiv:0704.0937},
year = {2009}
}
Comments
LaTeX2e, 16 pages; misprints are corrected, some proofs are extended