Deformed Covariant Quantum Phase Spaces as Hopf Algebroids

Understand

We consider the general D=4 (10+10)-dimensional kappa-deformed quantum phase space as given by Heisenberg double \mathcal{H} of D=4 kappa-deformed Poincare-Hopf algebra H.

• The standard (4+4) -dimensional kappa - deformed covariant quantum phase space spanned by kappa - deformed Minkowski coordinates and commuting momenta generators ({x}_{\mu },{p}_{\mu }) is obtained as the subalgebra of \mathcal{H}.
• We study further the property that Heisenberg double defines particular quantum spaces with Hopf algebroid structure.
• We calculate by using purely algebraic methods the explicite Hopf algebroid structure of standard kappa - deformed quantum covariant phase space in Majid-Ruegg bicrossproduct basis.