Central extensions of precrossed modules

被引:6
作者
Arias, D [1 ]
Ladra, M
机构
[1] Univ Leon, Dept Matemat, E-24071 Leon, Spain
[2] Univ Santiago de Compostela, Dept Algebra, E-15782 Santiago De Compostela, Spain
关键词
central extension; precrossed module; cohomology; Galois theory;
D O I
10.1023/B:APCS.0000040555.48968.64
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We classify the precrossed module central extensions using the second cohomology group of precrossed modules. We relate these central extensions to the relative central group extensions of Loday, and to other notions of centrality defined in general contexts. Finally we establish a Universal Coefficient Theorem for the (co)homology of precrossed modules, which we use to describe the precrossed module central extensions in terms of the generalized Galois theory developed by Janelidze.
引用
收藏
页码:339 / 354
页数:16
相关论文
共 20 条
[1]   Universal central extensions of precrossed modules and Milnor's relative K2 [J].
Arias, D ;
Ladra, M ;
Grandjeán, AR .
JOURNAL OF PURE AND APPLIED ALGEBRA, 2003, 184 (2-3) :139-154
[2]   Homology of precrossed modules [J].
Arias, D ;
Ladra, M ;
R-Grandjeán, A .
ILLINOIS JOURNAL OF MATHEMATICS, 2002, 46 (03) :739-754
[3]  
BARR M, 1969, LECT NOTES MATH, V80, P245
[4]   Central extensions in semi-abelian categories [J].
Bourn, D ;
Gran, M .
JOURNAL OF PURE AND APPLIED ALGEBRA, 2002, 175 (1-3) :31-44
[5]   (Co)homology of crossed modules [J].
Carrasco, P ;
Cegarra, AM ;
Grandjeán, AR .
JOURNAL OF PURE AND APPLIED ALGEBRA, 2002, 168 (2-3) :147-176
[6]   COHOMOLOGY THEORY IN ABSTRACT GROUPS .1. [J].
EILENBERG, S ;
MACLANE, S .
ANNALS OF MATHEMATICS, 1947, 48 (01) :51-78
[7]  
FREEZE R, 1987, LONDON MATH SOC LECT, V125
[8]  
Frohlich A., 1963, T AM MATH SOC, V109, P221
[9]  
Hilton P.J., 1971, Graduate Texts in Mathematics, V4
[10]   GALOIS THEORY AND A GENERAL NOTION OF CENTRAL EXTENSION [J].
JANELIDZE, G ;
KELLY, GM .
JOURNAL OF PURE AND APPLIED ALGEBRA, 1994, 97 (02) :135-161