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- 2016
Cocycle形变的整体维数
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Abstract:
摘要： 证明了如果H是整体维数为d的交换Hopf代数, 那么H的cocycle形变的整体维数小于等于d, 即交换Hopf代数的cocycle形变保持整体维数的有界性。
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
| [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 S<sub>3</sub> and S<sub>4</sub>[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] | BICHON J. Hopf-Galois objects and cogroupoids[J]. Revista De La Unión Matemática Argentina, 2014, 55(2):11-69. |
| [6] | LU Diming, WU Quanshui, ZHANG J J. Hopf algebras with rigid dualizing complexes[J]. Israel J Math, 2009, 169(1):89-108. |
| [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. |
