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| Gröbner-Shirshov Bases of Irreducible Modules of the Quantum Group of Type G2 |
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Citation： |
G. Usta,A. Obul.Gröbner-Shirshov Bases of Irreducible Modules of the Quantum Group of Type G2[J].Chinese Annals of Mathematics B,2016,37(3):427~440 |
| Page view： 1297
Net amount： 1040 |
Authors： |
G. Usta; A. Obul |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11061033, 11361056). |
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| Abstract： |
First, the authors give a Gr\"{o}bner-Shirshov basis of the
finite-dimensional irreducible module $V_q(\lambda)$ of the
Drinfeld-Jimbo quantum group $U_q(G_2)$ by using the double free
module method and the known Gr\"{o}bner-Shirshov basis of
$U_q(G_2).$ Then, by specializing a suitable version of $U_q(G_2)$
at $q=1,$ they get a Gr\"{o}bner-Shirshov basis of the universal
enveloping algebra $U(G_2)$ of the simple Lie algebra of type $G_2$
and the finite-dimensional irreducible $U(G_2)$-module $V(\lambda)$. |
Keywords： |
Quantum group, Gr\"{o}bner-Shirshov basis, Double free module,
Indecomposable module, Highest weight module |
Classification： |
16S15, 13P10, 17B37 |
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