x_R-Bialgebras associated with interative q-difference rings
x_R-Bialgebras associated with interative q-difference rings
复制标题
与交互 q 差环相关的 x_R-双代数
DOI：
10.1142/s0129167x13500304
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发表时间：
2013
影响因子：
0.6
通讯作者：
Makoto Yanagawa
中科院分区：
文献类型：
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作者：
Akira Masuoka;Makoto Yanagawa
实现Hardouin[迭代Q-差Galois理论，J.Reine Angew]所提出的可能性。644(2010)101-144]，我们证明了她自己的迭代q-差环的Picard-Vessiot(PV)理论是由Amano和Masuoka[Picard-Vessiot Expansion of Artin单模代数，J.Algebra285(2005)743-767]在余交换点Hopf代数上建立的(因此，更一般的)框架所覆盖的。一个要点是用某个余交换×R-双代数上的模来表示迭代q-差环R上的迭代q-差模。回想一下，×R-双代数的概念是由Sweedler[Groups of Simple Algeas，Publ.数学课。安装Hautesétods Science.44(1974)79-189]，作为双代数的推广。
Realizing the possibility suggested by Hardouin [Iterative q-difference Galois theory,J. Reine Angew. Math.644(2010) 101–144], we show that her own Picard–Vessiot (PV) theory for iterative q-difference rings is covered by the (consequently, more general) framework, settled by Amano and Masuoka [Picard–Vessiot extensions of artinian simple module algebras,J. Algebra285(2005) 743–767], of artinian simple module algebras over a cocommutative pointed Hopf algebra. An essential point is to represent iterative q-difference modules over an iterative q-difference ring R, by modules over a certain cocommutative ×R-bialgebra. Recall that the notion of ×R-bialgebras was defined by Sweedler [Groups of simple algebras,Publ. Math. Inst. Hautes Études Sci.44(1974) 79–189], as a generalization of bialgebras.