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<Emphasis Type="Italic">C</Emphasis>*-Homomorphisms and duality of <Emphasis Type="Italic">C</Emphasis>*-discrete quantum groups
Authors:Lining Jiang
Institution:(1) Beijing Institute of Technology, Beijing, China
Abstract:
Let
Open image in new window /></a> </div></figure> be a <em class=C*-discrete quantum group and let
Open image in new window /></a> </div></figure> be the discrete quantum group associated with <figure class=
Open image in new window /></a> </div></figure>. Suppose that there exists a continuous action of <figure class=
Open image in new window /></a> </div></figure> on a unital <em class=C*-algebra
Open image in new window /></a> </div></figure> so that <figure class=
Open image in new window /></a> </div></figure> becomes a <figure class=
Open image in new window /></a> </div></figure>-algebra. If there is a faithful irreducible vacuum representation <em class=π of
Open image in new window /></a> </div></figure> on a Hilbert space <em class=H =
Open image in new window /></a> </div></figure> with a vacuum vector Ω, which gives rise to a <figure class=
Open image in new window /></a> </div></figure>-invariant state, then there is a unique <em class=C*-representation (θ, H) of
Open image in new window /></a> </div></figure> supplemented by the action. The fixed point subspace of <figure class=
Open image in new window /></a> </div></figure> under the action of <figure class=
Open image in new window /></a> </div></figure> is exactly the commutant of <em class=θ(
Open image in new window /></a> </div></figure>).</div></td> </tr> <tr> <td align=
Keywords:discrete quantum group            C*-algebra            C*-homomorphism  duality
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