Geodesic
Extensions of racks and quandles
Homology, homotopy, and applications, Tome 7 (2005) no. 1, pp. 151-167.

Voir la notice de l'article provenant de la source International Press of Boston

A rack is a set equipped with a bijective, self-right-distributive binary operation, and a quandle is a rack which satisfies an idempotency condition. In this paper, we introduce a new definition of modules over a rack or quandle, and show that this definition includes the one studied by Etingof and Graña [9] and the more general one given by Andruskiewitsch and Graña [1]. We further show that this definition coincides with the appropriate specialisation of the definition developed by Beck [3], and hence that these objects form a suitable category of coefficient objects in which to develop homology and cohomology theories for racks and quandles. We then develop an Abelian extension theory for racks and quandles which contains the variants developed by Carter, Elhamdadi, Kamada and Saito [6, 7] as special cases.
DOI : 10.4310/HHA.2005.v7.n1.a8
Classification : 18E10, 18G15, 18G60
Keywords: racks, quandles, extensions, modules, homology, cohomology 
@article{HHA_2005_7_1_a8,
     author = {Nicholas Jackson},
     title = {Extensions of racks and quandles},
     journal = {Homology, homotopy, and applications},
     pages = {151--167},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2005},
     doi = {10.4310/HHA.2005.v7.n1.a8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2005.v7.n1.a8/}
}
TY  - JOUR
AU  - Nicholas Jackson
TI  - Extensions of racks and quandles
JO  - Homology, homotopy, and applications
PY  - 2005
SP  - 151
EP  - 167
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2005.v7.n1.a8/
DO  - 10.4310/HHA.2005.v7.n1.a8
LA  - en
ID  - HHA_2005_7_1_a8
ER  - 
%0 Journal Article
%A Nicholas Jackson
%T Extensions of racks and quandles
%J Homology, homotopy, and applications
%D 2005
%P 151-167
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2005.v7.n1.a8/
%R 10.4310/HHA.2005.v7.n1.a8
%G en
%F HHA_2005_7_1_a8
Nicholas Jackson. Extensions of racks and quandles. Homology, homotopy, and applications, Tome 7 (2005) no. 1, pp. 151-167. doi : 10.4310/HHA.2005.v7.n1.a8. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2005.v7.n1.a8/

Cité par Sources :