Title: Explicit Realization of Hopf Cyclic Cohomology Classes of Bicrossed Product Hopf Algebras
Speaker: Tao Yang (OSU)
Abstract: We construct a Hopf action, with an invariant trace, of a bicrossed product Hopf algebra $\mathcal{H}=\big( \mathcal{R}(G_2) \hspace{-2pt} \blacktriangleright\hspace{-2.8pt}\vartriangleleft \hspace{-2pt} \mathcal{U}({\mathfrak{g}}_1) \big)^{{\rm cop}}$ constructed from a matched pair of Lie groups $G_1$ and $G_2$, on a convolution algebra $\mathcal{A}=C_{c}^{\infty}(G_1)\rtimes G_2^{\delta}$. We give an explicit way to construct Hopf cyclic cohomology classes of our Hopf algebra $\mathcal{H}$ and then realize these classes in terms of explicit representative cocycles in the cyclic cohomology of the convolution algebra $\mathcal{A}$.