Equivariant spectral triple for the quantum group \(U_q(2)\) for complex deformation parameters (Q2684770)

In [\textit{X.-X. Zhang} and \textit{E. Y.-W. Zhao}, Linear Algebra Appl. 408, 244--258 (2005; Zbl 1093.46042)], the quantum group \(U_{q}(2)\) is introduced, where \(q\) is a non-real complex number with \(|q| \neq 1\). This paper under review provides a concrete definition of the Dirac operator on \(U_{q}(2)\). The Dirac operator is equivariant under the comultiplication action of \(U_{q}(2)\). Furthermore, the spectral triple defined by the Dirac operator is \(4^{+}\)-summable and even, and the Connes-Chern character is non-trivial.