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

S. V. Kozyrev

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arXiv · hep-th/9403059

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

S. V. Kozyrev

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Abstract

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 $Π$ is introdused. This means that the representation $Π$ is invariant under coproduct by arbitrary representation. Algebra of functions on the quantum group $SU_{q}(2)$ in the representation $Π$ is a factor of a type II$_{\infty}$. Formula for the trace in the representation $Π$ is given . The invariant integral of Woronovich on $SU_{q}(2)$ will take the form $\int f dμ= tr(f cc^{*})$.

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S. V. Kozyrev. 1994-03-09. The Stable Representation of the algebra of functions on the quantum group $SU_{q}(2)$. https://arxiv.org/abs/hep-th/9403059

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