In ref. [1],Fisher studied the Hopf-Jacobson radical for Hopf module algebras, in which,when k is a field, it is required that the Hopf algebra H is irreducible as a coalgebra;that is, H contains a unique simple subco...In ref. [1],Fisher studied the Hopf-Jacobson radical for Hopf module algebras, in which,when k is a field, it is required that the Hopf algebra H is irreducible as a coalgebra;that is, H contains a unique simple subcoalgebra k. In this note, we discuss the Hopf-展开更多
This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module ...This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category: and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give a sufficient and necessary condition for the braid of, H? to induce the braid of , or equivalently, the braid of , whereA is a quantum commutativeH-module algebra展开更多
文摘In ref. [1],Fisher studied the Hopf-Jacobson radical for Hopf module algebras, in which,when k is a field, it is required that the Hopf algebra H is irreducible as a coalgebra;that is, H contains a unique simple subcoalgebra k. In this note, we discuss the Hopf-
文摘This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category: and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give a sufficient and necessary condition for the braid of, H? to induce the braid of , or equivalently, the braid of , whereA is a quantum commutativeH-module algebra
