Regular Fréchet-Lie groups of invertible elements in some inverse limits of unital involutive Banach algebras.
Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres
It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2) and it is...