The Structure Theorems of Weak Hopf Algebras

REFERENCES

• Böhm , G. , Nill , F. , Szlachànyi , K. ( 1999 ). Weak Hopf algebras I. Integral theory and C*-structure . J. Algebra 221 : 385 – 438 .
   Web of Science ®Google Scholar
• Hayashi , T. ( 1993 ). Quantum group symmetry of partition functions of IRF models and its applications to Jones's index theory . Comm. Math. Phys. 157 : 331 – 345 .
   Web of Science ®Google Scholar
• Nikshych , D. , Vainerman , L. ( 2002 ). Finite quantum groupoids and their applications . Math. Sci. Res. Inst. Publ. 43 : 211 – 262 .
   Google Scholar
• Yamanouchi , T. ( 1994 ). Duality for generalized Kac algebras and a characteriztion of finite groupoid algebras . J. Algebra 163 : 9 – 50 .
   Web of Science ®Google Scholar
• Nikshych , D. ( 2000 ). A duality theorem for quantum groupoids . Contemp. Math. 267 : 237 – 243 .
   Google Scholar
• Zhang , L. Y. ( 2006 ). Maschke-type theorem and Morita context over weak Hopf algebras . Sci. China. 49 ( 5 ): 587 – 598 .
   Google Scholar
• Zhang , L. Y. , Zhu , S. L. ( 2004 ). Fundamental theorems of weak Doi–Hopf modules and semisimple weak smash product Hopf algebras . Comm. Algebra 32 ( 9 ): 3403 – 3415 .
   Web of Science ®Google Scholar
• Doi , Y. ( 1983 ). On the structure of relative Hopf modules . Comm. Algebra 11 ( 3 ): 243 – 255 .
   Web of Science ®Google Scholar
• Cai , Z. M. , Zhang , L. Y. ( 2007 ). The fundamental theorem about weak relative [C, H]-Hopf modules . Math. Notes 82 ( 4 ): 474 – 480 .
   Web of Science ®Google Scholar
• Ulbrich , L. H. ( 1990 ). Smash products and comodules of linear maps . Tsukuba J. Math. 14 ( 2 ): 371 – 378 .
   Google Scholar
• Montgomery , S. ( 1993 ). Hopf Algebras and Their Actions on Rings . CBMS, Lect. Notes . Vol. 82 . Providence , RI : Amer. Math. Soc .
   Google Scholar
• Böhm , G. ( 2000 ). Doi–Hopf modules over weak Hopf algebras . Comm. Algebra 28 ( 10 ): 4687 – 4698 .
   Web of Science ®Google Scholar
• Kadison , L. , Nikshych , D. ( 2001 ). Frobenius extensions and weak Hopf algebras . J. Algebra 244 : 312 – 342 .
   Web of Science ®Google Scholar
• Communicated by Lawrence Ein.
   Google Scholar