构造新的辫子交叉范畴

Constructing New Braided Crossed Category

设π是一个群,首先引入弱α-Yetter-Drinfeld模的概念,然后证明范畴WYD(H)π={HWYDHα}α∈π构成一个辫子交叉范畴.特别的,如果H是一个有限型π-三角弱Hopfπ-余代数,则可得一个对称的辫子交叉子范畴WYD(H)π.其次,如果H是一个有限型弱交叉Hopfπ-余代数,则可得WYD(H)π和拟三角弱Hopfπ-余代数D(H)的表示范畴是同构的.

Let π be a group. We first introduce the notion of weak α-Yetter-Drinfeld modules with α∈π. Then we show the category （H） = { Hgn }.α∈π forms a braided crossed category. Especially we get a symmetric subcategory by a firfite type π-triangular weak Hopf rc-coalgebra.