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Dergiler / International Electronic Journal of Algebra / 2009 / Cilt: 6 - Sayı: 6

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

Bing-liang SHEN
Shuan-hong WANG
Sayfa
74–94
Yayın Tarihi
2009-12-01
DOI
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Also we will apply above result to the representations category Rep(L) = LM of a quasitriangular weak Hopf algebra L.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let L be a weak Hopf algebra with a bijective antipode SL in the sense of [3].
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Also we will apply above result to the representations category Rep(L) = LM of a quasitriangular weak Hopf algebra L.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

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Bu Makaleye Atıf Yap

SHEN, B., WANG, S. (2009). WEAK HOPF ALGEBRA DUALITY IN WEAK YETTER-DRINFELD CATEGORIES AND APPLICATIONS. International Electronic Journal of Algebra, Cilt: 6 - Sayı: 6, 74–94. https://ajindex.com/articles/832544

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Kaynakça (10)

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  3. 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.
  4. Y. Doi, Hopf modules in Yetter-Drifeld categories, Comm. Algebra, 26(9) (1998), 3057-3070.
  5. P. Etingof, D. Nikshych, Dynamical quantum groups at roots of 1, Duke Math. J., 108 (2001), 135-168.
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  7. D. Nikshych, A duality theorem for quantum groupoids, Contemporary Math- ematics, 267 (2000), 237-243.
  8. D. Nikshych, V. Turaev, L. Vainerman, Invariants of knots and 3-manifolds from quantum groupoids, Topology and its application, 127 (2003), 91-123.
  9. D. Nikshych, L. Vainerman, A characterization of depth 2 subfactors of Π1 factors, J. Funct. Anal., 171 (2000), 278-307.
  10. M. Sweedler, Hopf Algebras, Benjamin, New York, 1969. 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)