基于弱Hopf代数的半单范畴的构造
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摘要
本文研究并刻画了交换环上弱Hopf代数、Yetter-Drinfeld模范畴的一些性质,给出了其能够做成半单范畴的充分条件.
We study the properties of the category of the Yetter-Drinfeld modules over a weak Hopf algebra, and give sufficient condition for the Yetter-Drinfeld category to be semisimple.
We study the properties of the category of the Yetter-Drinfeld modules over a weak Hopf algebra, and give sufficient condition for the Yetter-Drinfeld category to be semisimple.
引文
[1] Angiono I., Ardizzoni A., Menini C., Cohomology and coquasi-bialgebras in the category of Yetter-Drinfeld modules, Ann. Sc. Norm.Super. Pisa Cl. Sci., 2017,17:609-653.
[2] Bohm G., Doi-Hopf modules over weak Hopf algebras, Comm. Algebra, 2000, 28:4687-4698.
[3] Bohm G., Yetter-Drinfeld modules over weak multiplier bialgebras, Israel J. Math.,2015, 209:85-123.
[4] Bohm G., Nill F., Szlachányi K., Weak Hopf Algebras I, Integral Theory and C~*-Structure, J. Algebra, 1999,221:385-438.
[5] Caenepeel S., Wang D. G., Yin Y. M., Yetter-Drinfeld modules over weak bialgebras, Ann. Univ. FerraraSez.VII-Sc. Mat., 2005, LI:69-98.
[6] Dai L., Dong J, C., On Kaplansky's sixth conjecture, Rend. Semin. Mat. Univ. Padova, 2016, 135:1-20.
[7] Dong J. C., Wang S. H., On semisimple Hopf algebras of dimension 2q~3, J. Algebra, 2013, 375:97-108.
[8] Kassel C., Quantum Groups, Springer-Verlag, New York, 1995.
[9] Montgomery S., Hopf Algebras and Their Actions on Rings, CMBS Reg. Conf. Ser. in Math. 82, Am. Math.Soc., Providence, 1993.
[10] Nenciu A., The center constructions for weak Hopf algebras, Tsukaba J. Math.,2002, 26(1):189-204.
[11] Nikshych D., On the Structure of Weak Hopf Algebras, Adv. Math., 2002, 170(2):257-286.
[12] Nikshych D., Semisimple weak Hopf algebras, J. Algebra, 2004, 275(2):639-667.
[13] Nikshych D., Turaev V. G., Vainerman L., Invariants of knots and 3-manifolds from quantum groupoids,Topol. Appl., 2003, 127(1/2):91-123.
[14] Pfeiffer H., Tannaka-Krein reconstruction and a characterization of modular tensor categories, J. Algebra,2009, 321(12):3714-3763.
[15] Wang S. X., Wang S. H., Hom-Lie algebras in Yetter-Drinfeld categories, Comm. Algebra, 2014, 42:4526-4547.
[16] Zhu H. X., Wang S. H., Chen J. Z., Bicovariant differential calculi on a weak Hopf algebra, Taiwanese J.Math., 2014, 18(6):1679-1712.
[2] Bohm G., Doi-Hopf modules over weak Hopf algebras, Comm. Algebra, 2000, 28:4687-4698.
[3] Bohm G., Yetter-Drinfeld modules over weak multiplier bialgebras, Israel J. Math.,2015, 209:85-123.
[4] Bohm G., Nill F., Szlachányi K., Weak Hopf Algebras I, Integral Theory and C~*-Structure, J. Algebra, 1999,221:385-438.
[5] Caenepeel S., Wang D. G., Yin Y. M., Yetter-Drinfeld modules over weak bialgebras, Ann. Univ. FerraraSez.VII-Sc. Mat., 2005, LI:69-98.
[6] Dai L., Dong J, C., On Kaplansky's sixth conjecture, Rend. Semin. Mat. Univ. Padova, 2016, 135:1-20.
[7] Dong J. C., Wang S. H., On semisimple Hopf algebras of dimension 2q~3, J. Algebra, 2013, 375:97-108.
[8] Kassel C., Quantum Groups, Springer-Verlag, New York, 1995.
[9] Montgomery S., Hopf Algebras and Their Actions on Rings, CMBS Reg. Conf. Ser. in Math. 82, Am. Math.Soc., Providence, 1993.
[10] Nenciu A., The center constructions for weak Hopf algebras, Tsukaba J. Math.,2002, 26(1):189-204.
[11] Nikshych D., On the Structure of Weak Hopf Algebras, Adv. Math., 2002, 170(2):257-286.
[12] Nikshych D., Semisimple weak Hopf algebras, J. Algebra, 2004, 275(2):639-667.
[13] Nikshych D., Turaev V. G., Vainerman L., Invariants of knots and 3-manifolds from quantum groupoids,Topol. Appl., 2003, 127(1/2):91-123.
[14] Pfeiffer H., Tannaka-Krein reconstruction and a characterization of modular tensor categories, J. Algebra,2009, 321(12):3714-3763.
[15] Wang S. X., Wang S. H., Hom-Lie algebras in Yetter-Drinfeld categories, Comm. Algebra, 2014, 42:4526-4547.
[16] Zhu H. X., Wang S. H., Chen J. Z., Bicovariant differential calculi on a weak Hopf algebra, Taiwanese J.Math., 2014, 18(6):1679-1712.