Geodesic
Composition-diamond lemma for modules
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 59-76

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and "double-free" left modules (that is, free modules over a free algebra). We first give Chibrikov's Composition-Diamond lemma for modules and then we show that Kang-Lee's Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra $sl_2$, the Verma module over a Kac-Moody algebra, the Verma module over the Lie algebra of coefficients of a free conformal algebra, and a universal enveloping module for a Sabinin algebra. As applications, we also obtain linear bases for the above modules.
Classification : 13P10, 16D10, 16S15, 17A01, 17B67
Keywords: Gröbner-Shirshov basis; module; Lie algebra; Kac-Moody algebra; conformal algebra; Sabinin algebra 
@article{CMJ_2010__60_1_a3,
     author = {Chen, Yuqun and Chen, Yongshan and Zhong, Chanyan},
     title = {Composition-diamond lemma for modules},
     journal = {Czechoslovak Mathematical Journal},
     pages = {59--76},
     publisher = {mathdoc},
     volume = {60},
     number = {1},
     year = {2010},
     mrnumber = {2595070},
     zbl = {1224.16046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a3/}
}
TY  - JOUR
AU  - Chen, Yuqun
AU  - Chen, Yongshan
AU  - Zhong, Chanyan
TI  - Composition-diamond lemma for modules
JO  - Czechoslovak Mathematical Journal
PY  - 2010
SP  - 59
EP  - 76
VL  - 60
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a3/
LA  - en
ID  - CMJ_2010__60_1_a3
ER  - 
%0 Journal Article
%A Chen, Yuqun
%A Chen, Yongshan
%A Zhong, Chanyan
%T Composition-diamond lemma for modules
%J Czechoslovak Mathematical Journal
%D 2010
%P 59-76
%V 60
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a3/
%G en
%F CMJ_2010__60_1_a3
Chen, Yuqun; Chen, Yongshan; Zhong, Chanyan. Composition-diamond lemma for modules. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 59-76. http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a3/