Properties of Groups of Lie Type

IsSimple( G ) : GrpLie -> BoolElt

Returns true if the group of Lie type G is a simple group of Lie type, ie. if the underlying root datum is irreducible. Note that this does not necessarily mean that G is simple as an abstract group.

IsSimplyLaced( G ) : GrpLie-> BoolElt

Returns true if the group of Lie type G is simply laced, i.e. its Dynkin diagram contains no multiple bonds.

IsSemisimple( G ) : GrpLie-> BoolElt

Returns true if the group of Lie type G is semisimple.

IsAdjoint( G ) : GrpLie-> BoolElt

Returns true if the group of Lie type G is adjoint (ie. the isogeny group is trivial).

IsSimplyConnected( G ) : GrpLie-> BoolElt

Returns true if the group of Lie type G is simply connected (ie. the isogeny group is equal to the fundamental group, ie. the coisogeny group is trivial).