Gröbner-Shirshov bases for exceptional Lie algebras I Original Research Article

Gröbner-Shirshov bases for the exceptional Lie algebras G2 and F4, abstractly defined by generators and the Serre relations for the corresponding Cartan matrices over a field of characteristic ≠ 2, 3, are constructed. As an application, we obtain for G2 and F4 linear bases of Lyndon-Shirshov words in the generators. The calculation of the multiplication tables in terms of the constructed linear bases might be another application.