Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{...Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{H,R)-pseudoalgebras are studied by generalizing the aboveconstruction when(H,R)is a quasitrianglar Hopf algebra.A tthe same time,the(H,R)-pseudoalgebra is constructed byboth the usual algebra and the tensor product o f(H,R)-pseudoalgebras.Finally,some examples of the(H,R)-pseudoalgebra are given explicitly,and the conditions for aHopf algebra to be an(H,R)-pseudoalgebra(resp.Hpseudoalgebra)are discussed.展开更多
If an algebra A is quantum commutative with respect to the action of a quasitriangular Hopf algebra H, then the monoidal structure on the category HM of modules over H induces a monoidal structure on the category A#H ...If an algebra A is quantum commutative with respect to the action of a quasitriangular Hopf algebra H, then the monoidal structure on the category HM of modules over H induces a monoidal structure on the category A#H M modules over the associated smash product A #H. The condition under which the braiding structure of HM induces a braiding structure on A#H M is further investigated. Dually, the notion of quantum cocommutativity is introduced, and similar result in this dual situation is obtained展开更多
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK20171348)
文摘Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{H,R)-pseudoalgebras are studied by generalizing the aboveconstruction when(H,R)is a quasitrianglar Hopf algebra.A tthe same time,the(H,R)-pseudoalgebra is constructed byboth the usual algebra and the tensor product o f(H,R)-pseudoalgebras.Finally,some examples of the(H,R)-pseudoalgebra are given explicitly,and the conditions for aHopf algebra to be an(H,R)-pseudoalgebra(resp.Hpseudoalgebra)are discussed.
文摘If an algebra A is quantum commutative with respect to the action of a quasitriangular Hopf algebra H, then the monoidal structure on the category HM of modules over H induces a monoidal structure on the category A#H M modules over the associated smash product A #H. The condition under which the braiding structure of HM induces a braiding structure on A#H M is further investigated. Dually, the notion of quantum cocommutativity is introduced, and similar result in this dual situation is obtained
