INTERNAL q-HOMOLOGY OF CROSSED MODULES

Proceedings of the Edinburgh Mathematical Society

Manuel Ladra¹ 

[1] Ana M. Vieites

关键词: crossed module;    classifying space;    q-homology;    q-commutator;    q-centre;   

DOI  :  10.1017/S0013091503001044

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

For $q$ a non-negative integer, we introduce the internal $q$-homology of crossed modules and we obtain in the case $q=0$ the homology of crossed modules. In the particular case of considering a group as a crossed module we obtain that its internal $q$-homology is the homology of the group with coefficients in the ring of the integers modulo $q$.The second internal $q$-homology of crossed modules coincides with the invariant introduced by Grandjeán and López, that is, the kernel of the universal $q$-central extension. Finally, we relate the internal $q$-homology of a crossed module to the homology of its classifying space with coefficients in the ring of the integers modulo $q$.AMS 2000 Mathematics subject classification: Primary 18G50; 20J05. Secondary 18G30

【 授权许可】

Unknown