Deformed commutators on comodule algebras over coquasitriangular Hopf algebras

Zhongwei Wang, Guoyin Zhang, and Liangyun Zhang. "Deformed commutators on comodule algebras over coquasitriangular Hopf algebras." Colloquium Mathematicae 139.2 (2015): 165-183. <http://eudml.org/doc/283969>.

@article{ZhongweiWang2015,
abstract = {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.},
author = {Zhongwei Wang, Guoyin Zhang, Liangyun Zhang},
journal = {Colloquium Mathematicae},
keywords = {coquasitriangular Hopf algebras; comodule algebras; quantum commutators; quantum Lie algebras; injective dimension; projective dimension; Doi-Hopf modules},
language = {eng},
number = {2},
pages = {165-183},
title = {Deformed commutators on comodule algebras over coquasitriangular Hopf algebras},
url = {http://eudml.org/doc/283969},
volume = {139},
year = {2015},
}

TY - JOUR
AU - Zhongwei Wang
AU - Guoyin Zhang
AU - Liangyun Zhang
TI - Deformed commutators on comodule algebras over coquasitriangular Hopf algebras
JO - Colloquium Mathematicae
PY - 2015
VL - 139
IS - 2
SP - 165
EP - 183
AB - 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.
LA - eng
KW - coquasitriangular Hopf algebras; comodule algebras; quantum commutators; quantum Lie algebras; injective dimension; projective dimension; Doi-Hopf modules
UR - http://eudml.org/doc/283969
ER -