Abstract
In this paper, it is proved that the global dimension of a Yetter-Drinfel’d Hopf algebra coincides with the projective dimension of its trivial module k.
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References
Yetter D N. Quantum groups and representation of monoidal categories. Math Proc Cambridge Philos Soc, 108: 261–290 (1990)
Li L B, Zhang P. Twisted Hopf algebras, Ringel-Hall algebras and Green’s category. J Algebra, 231: 713–743 (2000)
Montgomery S. Hopf algebras and their actions on rings. CBMS Lecture Notes, Vol. 82. Providence, RI: Amer Math Soc, 1993
Radford D. The structure of Hopf algebras with a projection. J Algebra, 92: 322–347 (1985)
Doi Y. Hopf modules in Yetter-Drinfel’d categories. Comm Algebra, 26(9): 3057–3070 (1998)
Schauenburg P. Hopf modules and Yetter-Drinfel’d modules. J Algebra, 169: 874–890 (1994)
Sommerhäuser Y. Yetter-Drinfel’d Hopf Algebras over Groups of Prime Order. Lecture Notes in Math, Vol. 1789. Berlin: Springer, 2002
Lorenz M, Lorenz M. On crossed products of Hopf algebras. Proc Amer Math Soc, 123(1): 33–38 (1995)
Wang Y H, Chen X W. Construct non-graded bi-Frobenius algebras via quivers. Sci China Ser A, 50(3): 450–456 (2007)
Neuchl M, Schauenburg P. Reconstruction in braided categories and a notion of commutative bialgebras. J Pure Appl Algebra, 124: 241–259 (1998)
Sweedler M E. Hopf Algebras. New York: Benjamin, 1969
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This work was supported by National Natural Science Foundation of China (Grant No. 10726039), the Leading Academic Discipline Program and 211 Project for Shanghai University of Finance and Economics (the 3rd phase)
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Wang, Y. On global dimension of Yetter-Drinfel’d Hopf algebras. Sci. China Ser. A-Math. 52, 2154–2162 (2009). https://doi.org/10.1007/s11425-009-0057-z
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DOI: https://doi.org/10.1007/s11425-009-0057-z
Keywords
- Hopf algebras
- Yetter-Drinfel’d modules
- Yetter-Drinfel’d Hopf algebras
- projective dimension
- global dimension