On the Center of q - Deformed Algebra U ′ q ( so 3 ) Related to Quantum Gravity at q a Root of 1
نویسنده
چکیده
It is known that Fairlie–Odesskii algebra U ′ q(so3) appears as algebra of observables in quantum gravity in (2 + 1)-dimensional de Sitter space with space being torus. In this paper, we study the center of this algebra at q a root of 1. It turns out that Casimir elements in this case are algebraically dependent. Using realization of the algebra U ′ q(so3) in terms of quantized lengths of geodesics on torus with one hole, we find this dependence in an explicit form. It is expressed in terms of Chebyshev polynomials of the first kind. The properties of Casimir elements in the cyclic type representations are studied.
منابع مشابه
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