Dear Georg and all, Just to add that CoReLG and three other packages extending GAP's functionality for Lie algebras, namely LieRing, LiePRing and SLA, are included in GAP 4.7.2 distribution which was announced on Friday, and I'd like to encourage you to get CoReLG via upgrading to GAP 4.7.2 instead of trying to install it under GAP 4.6.4 which is dated May 2013.
Best wishes Alexander On 9 Dec 2013, at 21:03, Willem de Graaf <degr...@science.unitn.it> wrote: > Dear Georg, > > The problem is that the Cartan subalgebra that has been computed is not > split over the rationals. It is split over Q(i). > However, GAP does not take advantage of that. Recently we have written > a package, called corelg, which does manage to compute the root system > in this case (http://www.science.unitn.it/~corelg/): > > gap> L := LieAlgebraByStructureConstants( CF(4), T ); > <Lie algebra of dimension 14 over GaussianRationals> > gap> RootSystem(L); > <root system of rank 2> > > Best wishes, > > Willem de Graaf > > > On Sun, Dec 8, 2013 at 11:43 PM, Georg Beyerle <m...@gbeyerle.de> wrote: > >> Hello, >> >> the following table of structure constants (see below) appears to define >> a semi-simple Lie algebra. However, the call to RootSystem() fails: >> >> GAPInfo.Version = 4.6.4 >> GAPInfo.Architecture = i586-suse-linux-gnu-gcc-default32 >> Dimension( L ) = 14 >> SemiSimpleType( L ) : G2 >> Determinant( KillingMatrix( Basis( L ))) = 9618527719784448 >> CartanSubalgebra( L ) = Algebra( Rationals, [ v.1, v.8 ] ) >> #I the Cartan subalgebra of <L> in not split >> RootSystem( L ) = fail >> >> What am I missing? >> >> Thanks >> Georg >> >> >> Print( "GAPInfo.Version = ", GAPInfo.Version, "\n" ); >> Print( "GAPInfo.Architecture = ", GAPInfo.Architecture, "\n" ); >> SetInfoLevel( InfoAlgebra , 2 ); >> T:= EmptySCTable( 14, 0, "antisymmetric" );; >> SetEntrySCTable( T, 1, 2, [ -1 , 3 , -1 , 10 ] );; >> SetEntrySCTable( T, 1, 3, [ 1 , 2 , 1 , 9 ] );; >> SetEntrySCTable( T, 1, 4, [ 1 , 5 , -1 , 12 ] );; >> SetEntrySCTable( T, 1, 5, [ -1 , 4 , -1 , 11 ] );; >> SetEntrySCTable( T, 1, 6, [ 1 , 14 ] );; >> SetEntrySCTable( T, 1, 7, [ 1 , 6 , 1 , 13 ] );; >> SetEntrySCTable( T, 1, 9, [ 1 , 10 ] );; >> SetEntrySCTable( T, 1, 10, [ -1 , 9 ] );; >> SetEntrySCTable( T, 1, 11, [ 1 , 12 ] );; >> SetEntrySCTable( T, 1, 12, [ -1 , 11 ] );; >> SetEntrySCTable( T, 1, 13, [ 1 , 14 ] );; >> SetEntrySCTable( T, 1, 14, [ -2 , 6 , -2 , 13 ] );; >> SetEntrySCTable( T, 2, 3, [ -1 , 1 , -1 , 8 ] );; >> SetEntrySCTable( T, 2, 4, [ -1 , 6 , -1 , 13 ] );; >> SetEntrySCTable( T, 2, 5, [ -1 , 7 , -1 , 14 ] );; >> SetEntrySCTable( T, 2, 6, [ -1 , 11 ] );; >> SetEntrySCTable( T, 2, 7, [ 1 , 5 , -1 , 12 ] );; >> SetEntrySCTable( T, 2, 8, [ -1 , 10 ] );; >> SetEntrySCTable( T, 2, 10, [ 1 , 8 ] );; >> SetEntrySCTable( T, 2, 11, [ 1 , 6 ] );; >> SetEntrySCTable( T, 2, 12, [ 1 , 7 , 1 , 14 ] );; >> SetEntrySCTable( T, 2, 13, [ 1 , 4 , 1 , 11 ] );; >> SetEntrySCTable( T, 2, 14, [ 1 , 5 , -1 , 12 ] );; >> SetEntrySCTable( T, 3, 4, [ -1 , 7 ] );; >> SetEntrySCTable( T, 3, 5, [ -2 , 6 ] );; >> SetEntrySCTable( T, 3, 6, [ 2 , 5 ] );; >> SetEntrySCTable( T, 3, 7, [ 1 , 4 ] );; >> SetEntrySCTable( T, 3, 8, [ 1 , 9 ] );; >> SetEntrySCTable( T, 3, 9, [ -1 , 8 ] );; >> SetEntrySCTable( T, 3, 11, [ 1 , 7 , 1 , 14 ] );; >> SetEntrySCTable( T, 3, 12, [ -1 , 6 ] );; >> SetEntrySCTable( T, 3, 13, [ -1 , 5 ] );; >> SetEntrySCTable( T, 3, 14, [ -1 , 4 , -1 , 11 ] );; >> SetEntrySCTable( T, 4, 5, [ -1 , 8 ] );; >> SetEntrySCTable( T, 4, 6, [ 1 , 9 ] );; >> SetEntrySCTable( T, 4, 7, [ -2 , 3 , -2 , 10 ] );; >> SetEntrySCTable( T, 4, 8, [ 1 , 5 ] );; >> SetEntrySCTable( T, 4, 9, [ -1 , 6 ] );; >> SetEntrySCTable( T, 4, 10, [ 1 , 7 ] );; >> SetEntrySCTable( T, 4, 12, [ -1 , 1 , -1 , 8 ] );; >> SetEntrySCTable( T, 4, 13, [ -1 , 2 , -1 , 9 ] );; >> SetEntrySCTable( T, 4, 14, [ 1 , 3 , 1 , 10 ] );; >> SetEntrySCTable( T, 5, 6, [ -2 , 3 ] );; >> SetEntrySCTable( T, 5, 7, [ 1 , 9 ] );; >> SetEntrySCTable( T, 5, 8, [ -1 , 4 ] );; >> SetEntrySCTable( T, 5, 9, [ -1 , 7 ] );; >> SetEntrySCTable( T, 5, 10, [ -1 , 6 ] );; >> SetEntrySCTable( T, 5, 11, [ -1 , 1 , -1 , 8 ] );; >> SetEntrySCTable( T, 5, 13, [ 1 , 3 ] );; >> SetEntrySCTable( T, 5, 14, [ -1 , 2 , -1 , 9 ] );; >> SetEntrySCTable( T, 6, 7, [ 1 , 8 ] );; >> SetEntrySCTable( T, 6, 8, [ -1 , 7 ] );; >> SetEntrySCTable( T, 6, 9, [ 1 , 4 ] );; >> SetEntrySCTable( T, 6, 10, [ 1 , 5 ] );; >> SetEntrySCTable( T, 6, 11, [ -1 , 2 ] );; >> SetEntrySCTable( T, 6, 12, [ 1 , 3 ] );; >> SetEntrySCTable( T, 6, 14, [ 1 , 1 ] );; >> SetEntrySCTable( T, 7, 8, [ 1 , 6 ] );; >> SetEntrySCTable( T, 7, 9, [ 1 , 5 ] );; >> SetEntrySCTable( T, 7, 10, [ -1 , 4 ] );; >> SetEntrySCTable( T, 7, 11, [ -1 , 3 , -1 , 10 ] );; >> SetEntrySCTable( T, 7, 12, [ -1 , 2 , -1 , 9 ] );; >> SetEntrySCTable( T, 7, 13, [ 1 , 1 , 1 , 8 ] );; >> SetEntrySCTable( T, 8, 9, [ -2 , 10 ] );; >> SetEntrySCTable( T, 8, 10, [ 2 , 9 ] );; >> SetEntrySCTable( T, 8, 11, [ 1 , 12 ] );; >> SetEntrySCTable( T, 8, 12, [ -1 , 11 ] );; >> SetEntrySCTable( T, 8, 13, [ -1 , 7 , -1 , 14 ] );; >> SetEntrySCTable( T, 8, 14, [ 1 , 6 , 1 , 13 ] );; >> SetEntrySCTable( T, 9, 10, [ -2 , 8 ] );; >> SetEntrySCTable( T, 9, 11, [ -1 , 6 , -1 , 13 ] );; >> SetEntrySCTable( T, 9, 12, [ -1 , 14 ] );; >> SetEntrySCTable( T, 9, 13, [ 1 , 4 , 1 , 11 ] );; >> SetEntrySCTable( T, 9, 14, [ 1 , 12 ] );; >> SetEntrySCTable( T, 10, 11, [ -1 , 14 ] );; >> SetEntrySCTable( T, 10, 12, [ 1 , 6 , 1 , 13 ] );; >> SetEntrySCTable( T, 10, 13, [ 1 , 5 , -1 , 12 ] );; >> SetEntrySCTable( T, 10, 14, [ 1 , 11 ] );; >> SetEntrySCTable( T, 11, 12, [ 2 , 1 , 2 , 8 ] );; >> SetEntrySCTable( T, 11, 13, [ -1 , 2 , -1 , 9 ] );; >> SetEntrySCTable( T, 11, 14, [ -1 , 10 ] );; >> SetEntrySCTable( T, 12, 13, [ 1 , 3 , 1 , 10 ] );; >> SetEntrySCTable( T, 12, 14, [ -1 , 9 ] );; >> SetEntrySCTable( T, 13, 14, [ 1 , 1 ] );; >> >> L := LieAlgebraByStructureConstants( Rationals, T ); >> Print( "Dimension( L ) = ", Dimension( L ), "\n" ); >> typ := SemiSimpleType( L ); >> Print( "SemiSimpleType( L ) : ", typ, "\n" ); >> detKM := Determinant( KillingMatrix( Basis( L ))); >> Print( "Determinant( KillingMatrix( Basis( L ))) = ", detKM, "\n" ); >> H := CartanSubalgebra( L ); >> Print( "CartanSubalgebra( L ) = ", H, "\n" ); >> R := RootSystem( L ); >> Print( "RootSystem( L ) = ", R, "\n" ); >> >> _______________________________________________ >> Forum mailing list >> Forum@mail.gap-system.org >> http://mail.gap-system.org/mailman/listinfo/forum >> > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
