mrep

This file provides a matricial representations of the cubic algebra, here we use the GAP packge GBNP.

AA:=FreeAssociativeAlgebraWithOne(FIELD, "x", "a", "y", "b");
x:=AA.1;a:=AA.2; y:=AA.3; b:=AA.4;id:=One(AA);
rel_AA:=[a*x -id, x*a - id, b*y - id, y*b -id, (x-id)^3, (y-id)^3, (x*y - id)^3 , (a*y - id)^3 , (x^2*y - id)^3, (x*y^2 - id)^3];

rel_np:=List(rel_AA, GP2NP);
sb:=SGrobner(rel_np);
bqa:=BaseQA(sb,4, 0);

x:=MatrixQA(1, bqa, sb);
y:=MatrixQA(3, bqa, sb);
id:=x^0;

AA:= Algebra(FIELD, [ x,y ]) ;
I:=Ideal(AA, [(Comm(x,y) - x^0)^3]);
AA:=AA/I;
x:=AA.1;y:=AA.2;id:=x^0;
u:=x-id;v:=y-id;
BB:= Subalgebra(AA, [u,v]);

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