Let H be a cosemisimple Hopf algebra over an algebraically closed field k of characteristic zero. We show that if H is of type l ： 1 ＋ m ： p ＋ 1 ： q with p2 〈 q, or of type 1 ： 1 ＋ 1 ： m ＋ 1 ： n in the sens...Let H be a cosemisimple Hopf algebra over an algebraically closed field k of characteristic zero. We show that if H is of type l ： 1 ＋ m ： p ＋ 1 ： q with p2 〈 q, or of type 1 ： 1 ＋ 1 ： m ＋ 1 ： n in the sense of Larson and Radford, then H has the Frobenius property, that is, Kaplansky conjecture is true for these Hopf algebras.展开更多
There are various adjunctions between model(co)slice categories. The author gives a proposition to characterize when these adjunctions are Quillen equivalences. As an application, a triangle equivalence between the st...There are various adjunctions between model(co)slice categories. The author gives a proposition to characterize when these adjunctions are Quillen equivalences. As an application, a triangle equivalence between the stable category of a Frobenius category and the homotopy category of a non-pointed model category is given.展开更多
In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct t...In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gr¨obner-Shirshov basis for degenerate Ringel-Hall algebras of type F_4.展开更多
基金the National Natural Science Foundation(1024100210271113).
文摘Let H be a cosemisimple Hopf algebra over an algebraically closed field k of characteristic zero. We show that if H is of type l ： 1 ＋ m ： p ＋ 1 ： q with p2 〈 q, or of type 1 ： 1 ＋ 1 ： m ＋ 1 ： n in the sense of Larson and Radford, then H has the Frobenius property, that is, Kaplansky conjecture is true for these Hopf algebras.
基金supported by Jiangsu Normal University(No.JSNU12XLR025)
文摘There are various adjunctions between model(co)slice categories. The author gives a proposition to characterize when these adjunctions are Quillen equivalences. As an application, a triangle equivalence between the stable category of a Frobenius category and the homotopy category of a non-pointed model category is given.
基金supported by the National Natural Science Foundation of China(Nos.11361056,11271043,11471186)
文摘In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gr¨obner-Shirshov basis for degenerate Ringel-Hall algebras of type F_4.
