Abstract
Gröbner-Shirshov bases for the Lie algebras Bn, Cn, Dn, 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 that each of the previous algebras is isomorphic to a classical simple Lie algebra so2n+1(k), sp2n(k), so2nk respectively.
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