6533b860fe1ef96bd12c38d4
RESEARCH PRODUCT
Serial subalgebras of finitary Lie algebras
Felix LeinenFelix LeinenOrazio Puglisisubject
Discrete mathematicsPure mathematicsApplied MathematicsGeneral MathematicsLie algebraSubalgebraFinitaryRank (graph theory)Mathematics::Representation TheoryAscendantMathematicsdescription
A Lie subalgebra L of glK(V ) is said to be finitary if it consists of elements of finite rank. We show that, if L acts irreducibly on V , and if V is infinite-dimensional, then every non-trivial ascendant Lie subalgebra of L acts irreducibly on V too. When CharK 6= 2, it follows that the locally solvable radical of such L is trivial. In general, locally solvable finitary Lie algebras over fields of characteristic 6= 2 are hyperabelian.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-07-27 | Proceedings of the American Mathematical Society |