There are at least two kinds of generalization of Hopf algebra, i.e. pre-Hopf algebra and weak Hopf algebra. Correspondingly, we have two kinds of generalized bialgebras, almost bialgebra and weak bialgebra. Let L = ...There are at least two kinds of generalization of Hopf algebra, i.e. pre-Hopf algebra and weak Hopf algebra. Correspondingly, we have two kinds of generalized bialgebras, almost bialgebra and weak bialgebra. Let L = （L, ×, I, a, l, r） be a tensor category. By giving up I, l, r and keeping ×, a in L, the first author got so-called pre-tensor category L = （L, ×, a） and used it to characterize almost bialgebra and pre-Hopf algebra in Comm. in Algebra, 32（2）： 397-441 （2004）. Our aim in this paper is to generalize tensor category L = （L, ×, I, a, l, r） by weakening the natural isomorphisms l, r, i.e. exchanging the natural isomorphism ll^-1 = rr^-1 = id into regular natural transformations lll= l, rrr = r with some other conditions and get so-called weak tensor category so as to characterize weak bialgebra and weak Hopf algebra. The relations between these generalized （bialgebras） Hopf algebras and two kinds generalized tensor categories will be described by using of diagrams. Moreover, some related concepts and properties about weak tensor category will be discussed.展开更多
Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#...Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#H] under the additional assumption thatH was unimodular and used the Morita context to study the Smash product A#H. In1990, Cohen, Fischman and Montgomery showed that fix ring A^H and smash product展开更多
基金the Program for New Century Excellent Talents in University(No.04-0522)the National Natural Science Foundation of China(No.10571153)the Natural Science Foundation of Zhejiang Province of China(No.102028)
文摘There are at least two kinds of generalization of Hopf algebra, i.e. pre-Hopf algebra and weak Hopf algebra. Correspondingly, we have two kinds of generalized bialgebras, almost bialgebra and weak bialgebra. Let L = （L, ×, I, a, l, r） be a tensor category. By giving up I, l, r and keeping ×, a in L, the first author got so-called pre-tensor category L = （L, ×, a） and used it to characterize almost bialgebra and pre-Hopf algebra in Comm. in Algebra, 32（2）： 397-441 （2004）. Our aim in this paper is to generalize tensor category L = （L, ×, I, a, l, r） by weakening the natural isomorphisms l, r, i.e. exchanging the natural isomorphism ll^-1 = rr^-1 = id into regular natural transformations lll= l, rrr = r with some other conditions and get so-called weak tensor category so as to characterize weak bialgebra and weak Hopf algebra. The relations between these generalized （bialgebras） Hopf algebras and two kinds generalized tensor categories will be described by using of diagrams. Moreover, some related concepts and properties about weak tensor category will be discussed.
基金Project supported by the National Natural Science Foundation of China.
文摘Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#H] under the additional assumption thatH was unimodular and used the Morita context to study the Smash product A#H. In1990, Cohen, Fischman and Montgomery showed that fix ring A^H and smash product
