THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES

Year 2014, Volume: 15 Issue: 15, 41 - 55, 01.06.2014

Shuangjian Guo

https://doi.org/10.24330/ieja.266236

Abstract

In this paper, we introduce the concept of total quantum integrals
in the case of weak Hopf algebras and study the affineness criterion for weak
Yetter-Drinfel’d modules, which is a generalization of the results studied by
Menini and Militaru (J. Algebra, 247 (2002), 467-508).

Keywords

Weak Hopf algebra, total quantum integral, comodule algebra

References

• G. B¨ohm, Doi-Hopf modules over weak Hopf algebras, Comm. Algebra, 28 (2000), 4687–4698.
• G. B¨ohm, F. Nill and K. Szlach´anyi, Weak Hopf algebras I: Integral theory and C*-structure, J. Algebra, 221 (1999) 385–438.
• S. Caenepeel and E. De Groot, Modules over weak entwining structures, Con- temp. Math., 267 (2000), 31–54.
• S. Caenepeel, G. Militaru, Bogdan Ion and S. L. Zhu, Separable functors for the category of Doi-Hopf modules, applications, Adv. Math., 145 (1999), 239–290.
• S. Caenepeel, G. Militaru and S. L. Zhu, Crossed modules and Doi-Hopf mod- ules, Israel J. Math., 100 (1997), 221–247.
• S. Caenepeel, D. G. Wang and Y. M. Yin, Yetter-Drinfel’d modules over weak bialgebras, Ann. Univ. Ferrara-Sez. VII-Sc. Mat., 51 (2005), 69–98.
• Y. Doi and M. Takeuchi, Cleft comodule algebras for a bialgebra, Comm. Al- gebra, 13 (1985), 2137–2159.
• R. G. Larson and M. E. Sweedler, An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math., 91 (1969), 75–94.
• C. Menini and G. Militaru, Integrals, quantum Galois extensions and the affine- ness criterion for quantum Yetter-Drinfel’d modules, J. Algebra, 247 (2002), –508
• M. E. Sweedler, Hopf Algebras, Mathematics Lecture Note Series, W.A. Ben- jamin, Inc. New York, 1969.
• L. Y. Zhang, The structure theorem of weak comodule algebras, Comm. Alge- bra, 38 (2010), 254–260. Shuangjian Guo
• School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang, Guizhou 550025, China e-mail: [e-mail]