Abstract
First, the authors give a Grobner-Shirshov basis of the finite-dimensional irreducible module Vq(λ) of the Drinfeld-Jimbo quantum group Uq(G2) by using the double free module method and the known Grobner-Shirshov basis of Uq(G2). Then, by specializing a suitable version of Uq(G2) at q = 1, they get a Grobner-Shirshov basis of the universal enveloping algebra U(G2) of the simple Lie algebra of type G2 and the finite-dimensional irreducible U(G2)-module V (λ).
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