60.5 Properties of a Lie Algebra

is true if L is a Lie algebra such that each product of elements in L is zero, and false otherwise.

gap>  T:= EmptySCTable( 5, 0, "antisymmetric" );;
gap>  L:= LieAlgebraByStructureConstants( Rationals, T );
<Lie algebra of dimension 5 over Rationals>
gap> IsLieAbelian( L );
true

A Lie algebra L is defined to be (Lie) it nilpotent when its (Lie) lower central series reaches the trivial subalgebra.

gap> T:= EmptySCTable( 5, 0, "antisymmetric" );;
gap> L:= LieAlgebraByStructureConstants( Rationals, T );
<Lie algebra of dimension 5 over Rationals>
gap> IsLieNilpotent( L );                                
true

A Lie algebra L is defined to be (Lie) it solvable when its (Lie) derived series reaches the trivial subalgebra.

gap> T:= EmptySCTable( 5, 0, "antisymmetric" );;
gap> L:= LieAlgebraByStructureConstants( Rationals, T );
<Lie algebra of dimension 5 over Rationals>
gap> IsLieSolvable( L );
true

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