Left GB's
Quantum Algebra
Maximal Ideal
Algebraic Dependency in Quantum Algebras
The following non-standard quantum algebra arises from theoretical physics:

Uq(so3) = < x, y, z | yx = q xy - q1/2 z, zx = - (q+1) xz - q1/2(q+1) y, zy = q yz - q1/2x >.

If we consider q as a free parameter, Uq(so3) has only one central element Cq .

However, if we specialize q to the n-th root of unity, there appear three additional central elements. For n=3, the central elements are
Cq = q2 x2 + y2 + q2z2 + q1/2(1-q2)xyz,
C1 = 1/3 (x3 + x),
C2 = 1/3 (y3 + y),
C3 = 1/3 (z3 + z).

Task: Compute the polynomial, desribing the algebraic dependency of the central elements.

PLURAL Code

Answer:   Cq3 + 81q1/2(q+2)C1C2C3 - q Cq2 - 9(C12 + C22 + C32) .


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