Deformed commutators on quantum group module-algebras (Q1881122)

The author constructs quantum commutators on module algebras over quasi-triangular Hopf algebras. Their covariance and generalized antisymmetry and Leibniz properties will be shown. In the case of triangular Hopf algebras the module algebras obey a deformed Jacobi identity which turns them into quantum-Lie algebras. The author recalls known facts and provides some new results in the discussions on commutators, conjugacy, and module algebras over triangular Hopf algebras.