SavedAdd your journal

Journals / International Electronic Journal of Algebra / 2009 / Volume: 6 Issue: 6

WEAK HOPF ALGEBRA DUALITY IN WEAK YETTER-DRINFELD CATEGORIES AND APPLICATIONS

Bing-liang Shen
Shuan-hong Wang
Pages
—
Publication Date
2009-12-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also we will apply above result to the representations category Rep(L) = LM of a quasitriangular weak Hopf algebra L.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let L be a weak Hopf algebra with a bijective antipode SL in the sense of [3].
📊
Key Findings & Data:In this paper we show that if H is a finite-dimensional weak Hopf algebra in the weak Yetter-Drinfeld category L LWYD in the sense of [1], then its dual H∗ is also a weak Hopf algebra in L LWYD.
💡
Conclusion & Impact:Also we will apply above result to the representations category Rep(L) = LM of a quasitriangular weak Hopf algebra L.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Weak Hopf algebra · weak Yetter-Drinfeld categories · weak (co)module (co)algebras

Abstract

Let L be a weak Hopf algebra with a bijective antipode SL in the sense of [3]. In this paper we show that if H is a finite-dimensional weak Hopf algebra in the weak Yetter-Drinfeld category L LWYD in the sense of [1], then its dual H∗ is also a weak Hopf algebra in L LWYD. Also we will apply above result to the representations category Rep(L) = LM of a quasitriangular weak Hopf algebra L.

🔖

Cite This Article

Shen, B., Wang, S. (2009). WEAK HOPF ALGEBRA DUALITY IN WEAK YETTER-DRINFELD CATEGORIES AND APPLICATIONS. International Electronic Journal of Algebra, Volume: 6 Issue: 6. https://ajindex.com/articles/1588323

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. G. B¨ohm, Doi-Hopf modules over weak Hopf algebras, Comm. Algebra, 28 (2000), 4687-4698.
  2. G. B¨ohm, F. Nill, K. Szlach´anyi, Weak Hopf algebras I. Integral theory and C*-structure, J. Algebra, 221 (1999), 385-438.
  3. G. B¨ohm, K. Szlach´anyi, A coassociative C*-quantum group with nonintegral dimensions, Lett. in Math. Phys., 35 (1996), 437-456.
  4. S. Caenepeel, E. De Groot, Modules over weak entwining structures, Contem- porary Mathematics, 267 (2000), 31-54.
  5. S. Caenepeel, D.G. Wang, Y.M. Yin, Yetter-Drinfeld modules over weak bial- gebras, Ann. Univ. Ferrara Sez. VII - Sc. Mat., 51 (2005), 69-98.
  6. Y. Doi, Hopf modules in Yetter-Drifeld categories, Comm. Algebra, 26(9) (1998), 3057-3070.
  7. P. Etingof, D. Nikshych, Dynamical quantum groups at roots of 1, Duke Math. J., 108 (2001), 135-168.
  8. L. Kadison, D. Nikshych, Frobenius extensions and weak Hopf algebras, J. Algebra, 244 (2001), 312-342.
  9. D. Nikshych, A duality theorem for quantum groupoids, Contemporary Math- ematics, 267 (2000), 237-243.
  10. D. Nikshych, V. Turaev, L. Vainerman, Invariants of knots and 3-manifolds from quantum groupoids, Topology and its application, 127 (2003), 91-123.
  11. D. Nikshych, L. Vainerman, A characterization of depth 2 subfactors of Π1 factors, J. Funct. Anal., 171 (2000), 278-307.
  12. M. Sweedler, Hopf Algebras, Benjamin, New York, 1969.
  13. Bing-liang Shen and Shuan-hong Wang Department of Mathematics Southeast University Nanjing, Jiangsu 210096, P. R. of China e-mail: [email protected] (B.L. Shen), [email protected] (S.H. Wang)