Induced *-representations and $C^*$-envelopes of some quantum $*$-algebras

Philip A. Dowerk; Yurii Savchuk

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arXiv · 1206.2806

Induced -representations and $C^$-envelopes of some quantum $*$-algebras

Philip A. Dowerk·Yurii Savchuk

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Abstract

We consider three quantum algebras: the q-oscillator algebra, the Podles' sphere and the q-deformed enveloping algebra of $su(2).$ To each of these *-algebras we associate certain partial dynamical system and perform the "Mackey analysis" of *-representations developed in [SS]. As a result we get the description of "standard" irreducible *-representations. Further, for each of these examples we show the existence of a "$C^*$-envelope" which is canonically isomorphic to the covariance $C^*$-algebra of the partial dynamical system. Finally, for the q-oscillator algebra and the q-deformed $\cU(su(2))$ we show the existence of "bad" representations.

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BibTeX RIS

Philip A. Dowerk, Yurii Savchuk. 2012-06-13. Induced *-representations and $C^*$-envelopes of some quantum $*$-algebras. https://arxiv.org/abs/1206.2806

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