构造新的辫子交叉范畴
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摘要
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.
Letπbe a group.We first introduce the notion of weakα-Yetter-Drinfeld modules withα∈π.Then we show the category WYD(H)π={HWYDHα}α∈πforms a braided crossed category.Especially we get a symmetric subcategory by a finite type π-triangular weak Hopf π-coalgebra.
Letπbe a group.We first introduce the notion of weakα-Yetter-Drinfeld modules withα∈π.Then we show the category WYD(H)π={HWYDHα}α∈πforms a braided crossed category.Especially we get a symmetric subcategory by a finite type π-triangular weak Hopf π-coalgebra.
引文
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[11]马天水,景俊霞,景艳艳.一类交叉双积[J].河南师范大学学报:自然科学版,2014,42(2):16-20.
[12]焦争鸣,郭敏,夏正亮.Hom-T-smash积Hom-Hopf代数上的拟三角结构[J].河南师范大学学报:自然科学版,2015,43(1):1-7.
[13]Wang S H.New Turaev braided group categories and group Schur-Weylduality[J].Appl Categor Struct,2013,21(2):141-166.
[2]Bhm G,Nill F,Szlachnyi K.Weak Hopf algebras I:Integral theory and C*-structure[J].J Algebra,1999,221:385-438.
[3]Maclane S.Categories for the Working Mathematician[M].New York:Springer,1971.
[4]Virelizier A.Hopf group-coalgebras[J].J Pure App Algebra,2002,171:75-122.
[5]Turaev V.Homotopy Quantum Field Theory[M].Eürich:European Mathematical Society,2010.
[6]van Daele A,Wang S H.New braided crossed categories and Drinfeld quantum double for weak Hopfπ-coalgebras[J].Comm Algebra,2010,38:1019-1049.
[7]Freyd P J,Yetter D N.Braided compact closed categories with applications to low-dimensional topology[J].Adv Math,1989,77(2):156-182.
[8]Kirillov A J.On G-equivariant modular categories[J].arXiv:math,2004,QA/0401119.
[9]Virelizier A.Involutory Hopf group-coalgebras and flat bundles over 3-manifolds[J].Fund Math,2005,188:241-270.
[10]马天水,李海英.Hopf交叉积上的余拟三角结构[J].河南师范大学学报:自然科学版,2012,40(2):22-25.
[11]马天水,景俊霞,景艳艳.一类交叉双积[J].河南师范大学学报:自然科学版,2014,42(2):16-20.
[12]焦争鸣,郭敏,夏正亮.Hom-T-smash积Hom-Hopf代数上的拟三角结构[J].河南师范大学学报:自然科学版,2015,43(1):1-7.
[13]Wang S H.New Turaev braided group categories and group Schur-Weylduality[J].Appl Categor Struct,2013,21(2):141-166.