We focus on the classification of pointed p^3-dimensional Hopf algebras H over any algebraically closed field of prime characteristic p 〉 0. In particular, we consider certain cases when the group of grouplike elemen...We focus on the classification of pointed p^3-dimensional Hopf algebras H over any algebraically closed field of prime characteristic p 〉 0. In particular, we consider certain cases when the group of grouplike elements is of order p or p^2 that is, when H is pointed but is not connected nor a group algebra. The structures of the associated graded algebra gr H are completely described as bosonizations of graded braided Hopf algebras over group algebras, and most of the lifting structures of H are given. This work provides many new examples of （parametrized） non-commutative, non-cocommutative finite- dimensional Hopf algebras in positive characteristic.展开更多
文摘We focus on the classification of pointed p^3-dimensional Hopf algebras H over any algebraically closed field of prime characteristic p 〉 0. In particular, we consider certain cases when the group of grouplike elements is of order p or p^2 that is, when H is pointed but is not connected nor a group algebra. The structures of the associated graded algebra gr H are completely described as bosonizations of graded braided Hopf algebras over group algebras, and most of the lifting structures of H are given. This work provides many new examples of （parametrized） non-commutative, non-cocommutative finite- dimensional Hopf algebras in positive characteristic.
