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THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES

Year 2014, , 41 - 55, 01.06.2014
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).

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: shuangjguo@gmail.com
Year 2014, , 41 - 55, 01.06.2014
https://doi.org/10.24330/ieja.266236

Abstract

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: shuangjguo@gmail.com
There are 12 citations in total.

Details

Other ID JA25HN93JN
Journal Section Articles
Authors

Shuangjian Guo This is me

Publication Date June 1, 2014
Published in Issue Year 2014

Cite

APA Guo, S. (2014). THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES. International Electronic Journal of Algebra, 15(15), 41-55. https://doi.org/10.24330/ieja.266236
AMA Guo S. THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES. IEJA. June 2014;15(15):41-55. doi:10.24330/ieja.266236
Chicago Guo, Shuangjian. “THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES”. International Electronic Journal of Algebra 15, no. 15 (June 2014): 41-55. https://doi.org/10.24330/ieja.266236.
EndNote Guo S (June 1, 2014) THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES. International Electronic Journal of Algebra 15 15 41–55.
IEEE S. Guo, “THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES”, IEJA, vol. 15, no. 15, pp. 41–55, 2014, doi: 10.24330/ieja.266236.
ISNAD Guo, Shuangjian. “THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES”. International Electronic Journal of Algebra 15/15 (June 2014), 41-55. https://doi.org/10.24330/ieja.266236.
JAMA Guo S. THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES. IEJA. 2014;15:41–55.
MLA Guo, Shuangjian. “THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES”. International Electronic Journal of Algebra, vol. 15, no. 15, 2014, pp. 41-55, doi:10.24330/ieja.266236.
Vancouver Guo S. THE AFFINENESS CRITERION FOR WEAK YETTER-DRINFEL’D MODULES. IEJA. 2014;15(15):41-55.