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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-2-2,
author = {Zhongwei Wang and Guoyin Zhang and Liangyun Zhang},
title = {Deformed commutators on comodule algebras over coquasitriangular Hopf algebras},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {165-183},
zbl = {1332.16025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-2-2}
}
Zhongwei Wang; Guoyin Zhang; Liangyun Zhang. Deformed commutators on comodule algebras over coquasitriangular Hopf algebras. Colloquium Mathematicae, Tome 139 (2015) pp. 165-183. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-2-2/