Dirac Operator on the Standard Podles Quantum Sphere
  Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podle\'s quantum sphere: equivariant representation, chiral grading $\gamma$, reality structure $J$ and the Dirac operator $D$, which has bounded commutators with the elements of the algebra and satisfies the first order condition. 
Ludwik Dabrowski and Andrzej Sitarz