Geometric Dirac operator on noncommutative torus and $M_2(\mathbb{C})$

E. Lira-Torres, S. Majid

We solve for quantum-geometrically realised spectral triples or `Dirac operators' on the noncommutative torus ${\mathbb{C}}_{\theta }[T^2]$ and on the algebra $M_2(\mathbb{C})$ of $2\times 2$ matric…