Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-06-29
Zap.Nauchn.Semin.200:3-16,1992; J.Math.Sci.77:3137-3145,1995
Physics
High Energy Physics
High Energy Physics - Theory
Uppsala University preprint UUITP 12/1994, 12 pages, LaTeX file
Scientific paper
It is known that the involution corresponding to the compact form is incompatible with comultiplication for quantum groups at $|q|=1$. In this paper we consider the quantum algebra of functions on the deformed space $T^{*}G_{q}$ 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 $q\rightarrow 1$. The algebra of functions on $T^{*}G_{q}$ 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.
Alekseev Anton Yu.
Faddeev Ludvig D.
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