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 
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     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},
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     zbl = {1224.16046},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a3/}
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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/