G_2型量子群表示的Grbner-Shirshov基

Grbner-Shirshov Basis Represented by G_2-Type Quantum Group

用单李代数的泛包络代数表示的Grbner-Shirshov基方法,也就是Grbner-Shirshov对(pair)方法,来构造G2型量子群表示的Grbner-Shirshov基是非常苦难的。而用双自由模方法来构造G2型量子群的有限维不可约表示的Grbner-Shirshov基是非常方便的;以已知的G2型量子群的Grbner-Shirshov基为基础,用双自由模方法构造G2型量子群的不可约表示的Grbner-Shirshov基。

The construction of Grobner-Shirshov Basis represented by G2-type quantum group by Grobner- Shirshov Basis method represented by universal enveloping algebras of simple Lie algebras, i.e. Grobner-Shirshov pair method, is very difficult, however, the construction of Grobner-Shirshov Basis represented by finite dimensional irreducible of G2-type quantum group by double free modules is convenient. By taking Grobner- Shirshov Basis of G2-type quantum group as the basis, this paper uses double free modules method to construct Grobner-Shirshov Basis of irreducible representation of G2-type quantum group.