Exact calculability, semigroup of representations, and the stability property for representations of the algebra of functions on the quantum groupSU q(2)

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An operation of the coproduct of representations of a bialgebra is defined. The coproduct operation of representations for the Hopf algebra of functions on the quantum groupSUq(2) is investigated. For this Hopf algebra a representation II called the stable representation is constructed. This representation is invariant with respect to the coproduct with an arbitrary representation. An expression for the trace in the representation II is derived. The invariant Voronovich integal inSUq(2) takes the form ∫fdµ=tr(fcc*).