Left GB's
Quantum Algebra
Maximal Ideal
Gröbner Bases for Left and Two-Sided Ideals

Task: Compute left Gröbner bases for left and two-sided ideals given by generating sets.

Consider the algebra

U(sl2) = < e, f, h | fe = ef - h, he = eh + 2e, hf = fh - 2f >,

and two sets of generators
I2 = {e2, f2, h2-1} and I3 = {e3, f3, h3-4h} .

Solution: first we set up the algebra

ring r=0,(e,f,h),Dp;
matrix C[3][3];
matrix D[3][3];
C[1,2]=1; C[1,3]=1; C[2,3]=1;
D[1,2]=-h; D[1,3]=2e; D[2,3]=-2f;
system("PLURAL",C,D);
r;
==> // characteristic : 0
// number of vars : 3
// block 1 : ordering Dp
// : names e f h
// block 2 : ordering C
// noncommutative relations:
// fe=ef-h
// he=eh+2e
// hf=fh-2f

Computations for I2
Computations for I3

Sao Carlos, 08/02 http://www.singular.uni-kl.de