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A involution and dynamics for the q deformed quantum top

1992
11 pages
Published in:
  • Zap.Nauchn.Semin. 200 (1992) 3-16,
  • J.Math.Sci. 77 (1995) 3137-3145
e-Print:
Report number:
  • UUITP-12-1994
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Abstract:
It is known that the involution corresponding to the compact form is incompatible with comultiplication for quantum groups at ∣q∣=1|q|=1. In this paper we consider the quantum algebra of functions on the deformed space T ∗GqT~{*}G_{q} which includes both the quantum group and the quantum universal enveloping algebra as subalgebras. For this extended object we construct an anti-involution which reduces to the compact form ∗*-operation in the limit q→1q\rightarrow 1. The algebra of functions on T ∗GqT~{*}G_{q} endowed with the ∗*-operation may be viewed as an algebra of observables of a quantum mechanical system. The most natural interpretation for such a system is a deformation of the quantum symmetric top. We suggest a discrete dynamics for this system which imitates the free motion of the top.