张量型Hom-Hopf代数的余ribbon元
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摘要
定义并讨论张量型Hom-Hopf代数的广义Hom余模范畴,利用Tannaka型对偶方法,刻画其刚性结构与平衡结构,进一步给出其为ribbon范畴的等价条件,并引入余ribbon元的定义.
We defined and discussed the category of generalized Hom-comodules of a monoidal Hom-Hopf algebra.We used the Tannaka dual method to describe the rigid and balanced structures.Furthermore,we gave equivalent conditions of the ribbon category,and introduced the definition of the coribbon forms.
We defined and discussed the category of generalized Hom-comodules of a monoidal Hom-Hopf algebra.We used the Tannaka dual method to describe the rigid and balanced structures.Furthermore,we gave equivalent conditions of the ribbon category,and introduced the definition of the coribbon forms.
引文
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[8]MAKHLOUF A,SILVESTROV S D.Notes on 1-Parameter Formal Deformations of Hom-Associative and Hom-Lie Algebras[J].Forum Mathematicum,2010,22(4):715-739.
[9]YOU Miman,WANG Shuanhong.A Generalized Double Crossproduct for Monoidal Hom-Hopf Algebras and the Drinfeld Double[J].Colloquium Mathematicum,2017,146:213-238.
[10]CAENEPEEL S,GOYVAERTS I.Monoidal Hom-Hopf Algebras[J].Communications in Algebra,2011,39(6):2216-2240.
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[12]MA Tianshui,ZHENG Huihui.Some Results on Rota-Baxter Monoidal Hom-Algebras[J].Results in Mathematics,2017,72(1/2):145-170.
[13]KASSEL C.Quantum Groups[M].New York:Springer-Verlag,1995.
[2]HU Naihong.q-Witt Algebras,q-Lie Algebras,q-Holomorph Structure and Representations[J].Algebra Colloquium,1999,6(1):51-70.
[3]LARSSON D,SILVESTROV S D.Quasi-Lie Algebras[J].Contemporary Mathematics,2005,391:241-248.
[4]LARSSON D,SILVESTROV S D.Quasi-Hom-Lie Algebras,Central Extensions and 2-Cocycle-Like Identities[J].Journal of Algebra,2005,288(2):321-344.
[5]HARTWIG J T,LARSSON D,SILVESTROV S D.Deformations of Lie Algebras Usingσ-Derivations[J].Journal of Algebra,2006,295(2):314-361.
[6]MAKHLOUF A,SILVESTROV S D.Hom-Algebras Structures[J].Journal of Generalized Lie Theory and Applications,2008,2(2):51-64.
[7]MAKHLOUF A,SILVESTROV S D.Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras[M]//SILVESTROV S D,PAAL E,ABRAMOV V,et al,ed.Generalized Lie Theory in Mathematics,Physics and Beyond.Berlin:Springer-Verlag,2008:189-206.
[8]MAKHLOUF A,SILVESTROV S D.Notes on 1-Parameter Formal Deformations of Hom-Associative and Hom-Lie Algebras[J].Forum Mathematicum,2010,22(4):715-739.
[9]YOU Miman,WANG Shuanhong.A Generalized Double Crossproduct for Monoidal Hom-Hopf Algebras and the Drinfeld Double[J].Colloquium Mathematicum,2017,146:213-238.
[10]CAENEPEEL S,GOYVAERTS I.Monoidal Hom-Hopf Algebras[J].Communications in Algebra,2011,39(6):2216-2240.
[11]LIU Ling,SHEN Bingliang.Radford’s Biproducts and Yetter-Drinfeld Modules for Monoidal Hom-Hopf Algebras[J].Journal of Mathematical Physics,2014,55:031701-1-031701-16.
[12]MA Tianshui,ZHENG Huihui.Some Results on Rota-Baxter Monoidal Hom-Algebras[J].Results in Mathematics,2017,72(1/2):145-170.
[13]KASSEL C.Quantum Groups[M].New York:Springer-Verlag,1995.