First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bi...First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.展开更多
It is shown that the dual bialgebra of any quasitriangular bialgebra is braided, and the dual bialgebra of some braided bialgebra is quasitriangular.Also it is proved that every nondegenerate finite dimensional braid...It is shown that the dual bialgebra of any quasitriangular bialgebra is braided, and the dual bialgebra of some braided bialgebra is quasitriangular.Also it is proved that every nondegenerate finite dimensional braided (dually, quasitriangular) bialgebra has an antipode.展开更多
文摘First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.
文摘It is shown that the dual bialgebra of any quasitriangular bialgebra is braided, and the dual bialgebra of some braided bialgebra is quasitriangular.Also it is proved that every nondegenerate finite dimensional braided (dually, quasitriangular) bialgebra has an antipode.
