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Applications: Algebraic Dependency In Quantum Algebra
This nonstandard quantum algebra arised from the 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 at the n-th root of unity, there will appear three additional central elements. If n=3, these 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)


Lille, 08-07-02 http://www.singular.uni-kl.de