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TitleComposition-diamond lemma for modules.
Author(s) Yu-Fu Chen, Chanyan Zhong
TypeArticle in Journal
AbstractWe 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.
ISSN0011-4642; 1572-9141/e
URL http://link.springer.com/article/10.1007%2Fs10587-010-0018-2
LanguageEnglish
JournalCzech. Math. J.
Volume60
Number1
Pages59--76
PublisherSpringer, Berlin/Heidelberg
Year2010
Edition0
Translation No
Refereed No
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