Gröbner Bases
Syzygies
Resolutions
Quantum Alg.
Left Maximality
Max. Twosided
Free Resolutions

Task: Compute left syzygies and free resolutions for left modules.

Consider the algebra

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

and the set of left generators I = {e2, f}.

Set up the algebra

ring r=0,(e,f,h),Dp;
matrix D[3][3];
D[1,2]=-h; D[1,3]=2e; D[2,3]=-2f;
system("PLURAL",1,D);

Computations of free resolutions

KL, 06/03 http://www.singular.uni-kl.de