Equivariant spectral triple for the compact quantum group $U_q(2)$ for complex deformation parameters

Abstract: Let $q=|q|e^{i\pi\theta}$ be a nonzero complex number such that $|q|\neq 1$, and consider the compact quantum group $U_q(2)$. In this talk, we discuss a complete list of inequivalent irreducible representations of $U_q(2)$ and its Peter-Weyl decomposition. Then, for $\theta\notin\mathbb{Q}\setminus\{0,1\}$ we discuss the $K$-theory of the underlying $C^*$-algebra $C(U_q(2))$, and a spectral triple which is equivariant under the comultiplication action of $U_q(2)$. The spectral triple obtained here is even, $4^+$-summable, non-degenerate, and the Dirac operator acts on two copies of the $L^2$-space of $U_q(2)$. The Chern character of the associated Fredholm module is nontrivial.

This is a joint work with Bipul Saurabh.

high energy physicsmathematical physicsquantum algebra

Audience: researchers in the topic

Mathematical Physics Seminar

Series comments: Description: Noncommutative geometry, field theory, gravity.