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

摘要

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 Yu. Savchuk and K. Schmüdgen, Unbounded induced representations of *-algebras, Algebr. Represent. Theory, DOI: 10.1007/s10468-011-9310-6. 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 U(su(2)) we show the existence of "bad" representations.