Dirac operators on the fuzzyAdS2with the spins 12 and 1
It is shown here how the pseudo chirality and Dirac operators with the spins 12 and 1 on the commutative and fuzzy AdS2 should be constructed. The finite-dimensional and nonunitary representations of SU(1, 1) carrying the spin degrees of freedom 12 and 1 are used for the Dirac fields on commutative and fuzzy AdS2. In the fuzzy case, an explicit description of pseudo generalization of the Ginsparg-Wilson algebra is used to construct projective modules. The projector couplings left angular momentum and spin on the fuzzy AdS2 are used to produce minimum total angular momenta. They are realized by the first two and three representations of the total angular momentum for the spins 12 and 1, respectively. The pseudo projectors, the pseudo chirality, and Dirac operators with the spins 12 and 1 on the fuzzy AdS2 tend to their corresponding operators in the commutative limit.