Hopf-Galois systems

被引:15
作者
Bichon, J [1 ]
机构
[1] Univ Pau & Pays Adour, Lab Math Appl, IPRA, F-64000 Pau, France
关键词
Hopf-Galois extension; monoidal equivalence of comodule categories;
D O I
10.1016/S0021-8693(03)00140-6
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We introduce the concept of Hopf-Galois system, a reformulation of the notion of Galois extension of the base field for a Hopf algebra. The main feature of our definition is a generalization of the antipode of an ordinary Hopf algebra. We present several examples which indicate that although our axiomatic is slightly more complicated than the classical one, it is also more natural and easier to handle with. The main application of Hopf-Galois systems is the construction of monoidal equivalences between comodule categories. (C) 2003 Elsevier Science (USA). All rights reserved.
引用
收藏
页码:565 / 581
页数:17
相关论文
共 24 条
[1]   QUANTUM DEFORMATIONS OF GLN [J].
ARTIN, M ;
SCHELTER, W ;
TATE, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (8-9) :879-895
[2]  
Banica T, 1997, COMMUN MATH PHYS, V190, P143, DOI 10.1007/s002200050237
[3]   Some new deformations of the symmetric group [J].
Bichon, J .
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (09) :761-764
[4]   Cosovereign Hopf algebras [J].
Bichon, J .
JOURNAL OF PURE AND APPLIED ALGEBRA, 2001, 157 (2-3) :121-133
[5]  
BICHON J, IN PRESS COMM ALGEBR
[6]  
DOI Y, 1993, COMMUN ALGEBRA, V21, P1731, DOI 10.1080/00927879308824649
[7]   THE QUANTUM GROUP OF A NONDEGENERATE BILINEAR FORM [J].
DUBOISVIOLETTE, M ;
LAUNER, G .
PHYSICS LETTERS B, 1990, 245 (02) :175-177
[8]   Deformation of a Kac algebra by an Abelian subgroup [J].
Enock, M ;
Vainerman, L .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1996, 178 (03) :571-595
[9]  
JOYAL A, 1991, LECT NOTES MATH, V1488, P413
[10]  
Kassel C., 1995, GTM, V155