Geodesic
Composition-diamond lemma for modules
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 59-76 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     title = {Composition-diamond lemma for modules},
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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/

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