Invariants of Lie Algebras with Fixed Structure of Nilradicals

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dc.creatorBoyko, Vyacheslav
dc.creatorPatera, Jiri
dc.creatorPopovych, Roman
dc.date2006-06-19
dc.date2006-12-13
dc.date.accessioned2026-07-07T07:16:55Z
dc.date.available2026-07-07T07:16:55Z
dc.descriptionAn algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras, here the effectiveness of the algorithm is demonstrated by its application to computation of invariants of solvable Lie algebras of general dimension $n<\infty$ restricted only by a required structure of the nilradical. Specifically, invariants are calculated here for families of real/complex solvable Lie algebras. These families contain, with only a few exceptions, all the solvable Lie algebras of specific dimensions, for whom the invariants are found in the literature.
dc.descriptionLaTeX2e, 19 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0606045
dc.identifierhttp://arxiv.org/abs/math-ph/0606045
dc.identifierJ. Phys. A 40 (2007), 113-130
dc.identifierdoi:10.1088/1751-8113/40/1/006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113764
dc.subjectMathematical Physics
dc.subjectRepresentation Theory
dc.subject17B05; 17B10; 17B30; 22E70; 58D19; 81R05
dc.titleInvariants of Lie Algebras with Fixed Structure of Nilradicals
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