Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres
Tom 93 / 2011
Banach Center Publications 93 (2011), 225-240
MSC: Primary 58B34; Secondary 17B37.
DOI: 10.4064/bc93-0-18
Streszczenie
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 shown that the failure of the real structure to satisfy the commutant property is related to the failure of the universal R-matrix operator to be unitary.