JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 39-43.doi: 10.6040/j.issn.1671-9352.0.2015.428

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Global dimensions of cocycle deformations

YU Xiao-lan   

  1. College of Science, Hangzhou Normal University, Hangzhou 310036, Zhejiang, China
  • Received:2015-08-25 Online:2016-08-20 Published:2016-08-08

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Abstract: Let H be a commutative Hopf algebra with global dimension d. It is proved that the global dimension of any cocycle deformation of H is at most d. That is, cocycle deformations of commutative Hopf algebras preserve the boundedness of global dimensions.

Key words: Hopf algebra, global dimension, cocycle deformation

CLC Number: 

  • O154
[1] MASUOKA A. Abelian and non-abelian second cohomologies of quantized enveloping algebras[J]. J Algebra, 2007, 320(1):1-47.
[2] IGLESIAS A G, MOMBELLI M. Representations of the category of modules over pointed Hopf algebras over S3 and S4[J]. Pacific J Math, 2010, 252(2):343-378.
[3] GOODEARL K R, ZHANG J J. Homological properties of quantized coordinate rings of semisimple groups[J]. Proceedings of the London Mathematical Society, 2007, 94(5):647-671.
[4] KIRKMAN E, KUZMANOVICH J, ZHANG J J. Gorenstein subrings of invariants under Hopf algebra actions[J]. J Algebra, 2009, 322(10):3640-3669.
[5] LU Diming, WU Quanshui, ZHANG J J. Hopf algebras with rigid dualizing complexes[J]. Israel J Math, 2009, 169(1):89-108.
[6] BICHON J. Hopf-Galois objects and cogroupoids[J]. Revista De La Unión Matemática Argentina, 2014, 55(2):11-69.
[7] BICHON J. Hochschild homology of Hopf algebras and free Yetter-Drinfeld resolutions of the counit[J]. Compositio Mathematica, 2012, 149(4):658-678.
[8] BICHON J. Gerstenhaber-Schack and Hochschild cohomologies of co-Frobenius Hopf algebras[J/OL]. Eprint Arxiv, 2014. arXiv.org> math> arXiv:1411.1942.
[9] CAENEPEEL S, GUÉDÉNON T. Semisimplicity of the categories of Yetter-Drinfeld modules and Long dimodules[J]. Comm Algebra, 2004, 32(4):2767-2781.
[10] ANDRUSKIEWITSCH N, SCHNEIDER H J. A characterization of quantum groups[J]. Journal Für Die Reine Und Angewandte Mathematik, 2002, 2004(577):81-104.
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