[GAP Forum] semisimple type and chevalley basis

[R.N. Tsai]

Dear gap-forum,

I define a lie algebra which I know to be equivalent to type "A1".
I was hoping to have gap calculate a chavalley basis for this, but
this doesn't seem to be possible; even though gap recognizes the
algebra as "A1" (using SemiSimpleType). Is there a way around this?
Thanks,
R.N.

mats:=
[ [ [ 0, -1, 0 ], [ 1, 0, 0 ], [ 0, 0, 0 ] ], 
  [ [ 0, 0, -1 ], [ 0, 0, 0 ], [ 1, 0, 0 ] ], 
  [ [ 0, 0, 0 ], [ 0, 0, -1 ], [ 0, 1, 0 ] ] ];

alg:=LieAlgebra(Rationals,mats);

gap recognizes the algebra as "A1"

gap> SemiSimpleType(alg);
"A1"

but it has trouble with its chevalley basis

gap> ChevalleyBasis(alg);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `PositiveRoots' on 1 arguments called fr\
om
PositiveRoots( R ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;