Gröbner-Shirshov bases for exceptional Lie algebras. I (Q1295659)

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.