Deformed commutators on comodule algebras over coquasitriangular Hopf algebras
Volume 139 / 2015
Colloquium Mathematicum 139 (2015), 165-183 MSC: Primary 16T05; Secondary 81R50. DOI: 10.4064/cm139-2-2
We construct quantum commutators on comodule algebras over coquasitriangular Hopf algebras, so that they are quantum group coinvariant and have the generalized antisymmetry and Leibniz properties. If the coquasitriangular Hopf algebra is additionally cotriangular, then the quantum commutators satisfy a generalized Jacobi identity, and turn the comodule algebra into a quantum Lie algebra. Moreover, we investigate the projective and injective dimensions of some Doi-Hopf modules over a quantum commutative comodule algebra.