Adding to the previous answer: Actually in its original form due to Eichler and Kneser one uses not $Pin$ but the spin group, which is the two fold simply connected cover of the special orthogonal group and has its name from its use in quantum theory.
Adding to the previous answer: Actually in its original form due to Eichler and Kneser one uses not $Pin$ but the spin group, which is the two fold simply connected cover of the special orthogonal group and has its name from its use in quantum theory.