Gröbner-Shirshov bases for exceptional Lie algebras. I
type: Item
instance of: scholarly article
title: Gröbner-Shirshov bases for exceptional Lie algebras. I
zbMATH Open document ID: 0923.17014
DOI: 10.1016/S0022-4049(97)00180-1
author: V. Pereyra
published in: Journal of Pure and Applied Algebra
publication date: 1999-08-18T00:00:00Z
review text: In the earlier articles [Int. J. Algebra Comput. 6, No. 4, 389-400; 401-412 (1996; Zbl 0866.17007; Zbl 0866.17008], the authors had enlarged the Serre relations of types \(A_n\), \(B_n\), \(C_n\), \(D_n\), over a field of characteristic \(\neq 2,3\) to a Gröbner-Shirshov basis for the corresponding Lie algebra. In the article under review the authors do the same for the Serre relations of the exceptional types \(G_2\) and \(F_4\). The Gröbner-Shirshov basis for algebras \(G_2\) and \(F_4\) constructed in the article consists of 25 and 142 relations respectively. As an application, the authors obtain for \(G_2\) and \(F_4\) linear bases of Lyndon-Shirshov words in the generators.
Mathematics Subject Classification ID: 17B25
zbMATH DE Number: 1308274
zbMATH Keywords: Lie algebra
zbMATH Keywords: Gröbner-Shirshov basis
zbMATH Keywords: Lyndon-Shirshov words
reviewed by: Boris Vernikov
MaRDI profile type: Publication
Wikidata QID: Q115340077
cites work: SERRE RELATIONS AND GRÖBNER-SHIRSHOV BASES FOR SIMPLE LIE ALGEBRAS II
cites work: Standard Lyndon Bases of Lie Algebras and Enveloping Algebras
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description: scientific article; zbMATH DE number 1308274