A note on the classification of nine dimensional Lie algebras with nontrivial Levi decomposition

Abstract

The generalized Casimir invariants of real indecomposable Lie algebras admitting a nontrivial Levi decomposition are determined. 1 J 2 3 , I• Invariants of subalgebra:• Semi-invariance conditions:• Invariants of L p,q,r 9,13• Invariants of subalgebra:• Semi-invariance conditions:• Semi-invariance conditions:• Invariants of L p,q 9,17• Semi-invariance conditions:• Invariants of subalgebra:• Semi-invariance conditions:• Invariants of L p,q 9,32• Invariants of subalgebra:• Semi-invariance conditions:X 9 (J 1 ) = −J 1 , X 8 (J 2 ) = −2J 2 , X 9 (J 3 ) = −pJ 3 , X 9 (J 4 ) = −J 3 − pJ 4 .

Subalgebras of the rank two semisimple Lie algebras

“…s 8,1 , nilradical n 6,18 Classification of Levi decomposable algebras. The Levi decomposable algebras up to dimension 9 were classified by Turkowski[Tur88,Tur90], with some small omissions identified by Campoamor-Strusberg[CS09]. A detailed description of the classification, and general properties of Levi decomposable algebras is contained inŠnobl and Winternitz[ŠW14].…”

Integrabilidad de sistemas no lineales hamiltonianos con N grados de libertad

“…Casimir Operators play a crucial role in many modern physical theories, and the literature concerning its explicit forms and properties for many Lie algebras can be traced back from, for instance, [1,33,34,43,44,58,59,60,61,62,103,118,139,140,141,145,159,170].…”