The Stable Representation of the algebra of functions on the quantum group $SU_{q}(2)$

Details The Stable Representation of the algebra of functions on the quantum group $SU_{q}(2)$ The Stable Representation of the algebra of functions on the quantum group $SU_{q}(2)$

1994-03-09

arxiv.org/abs/hep-th/9403059v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

An operation of a coproduct of representations of a bialgebra is defined. The coproduct operation for representations of the Hopf algebra of functions on the quantum group $SU_{q}(2)$ is investigated. A notion of a stable representation $\Pi$ is introdused. This means that the representation $\Pi$ is invariant under coproduct by arbitrary representation. Algebra of functions on the quantum group $SU_{q}(2)$ in the representation $\Pi$ is a factor of a type II$_{\infty}$. Formula for the trace in the representation $\Pi$ is given . The invariant integral of Woronovich on $SU_{q}(2)$ will take the form $\int f d\mu = tr(f cc^{*})$.

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