Equivariant spectral triple for the quantum group Uq(2) for complex deformation parameters

Let q = vertical bar q vertical bar e(i pi theta) be a nonzero complex number such that vertical bar q vertical bar not equal 1 and consider the compact quantum group U-q(2). For theta is not an element of Q \ {0, 1}, we obtain the K-theory of the underlying C*-algebra C(U-q(2)). We construct a spectral triple on U-q(2) which is equivariant under its own comultiplication action. 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 K-homology class of the associated Fredholm module is shown to be nontrivial. (c) 2023 Elsevier B.V. All rights reserved.