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| On the Variations of $G_2% |
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Citation： |
LIU Dong,LIN Lei.On the Variations of $G_2%[J].Chinese Annals of Mathematics B,2003,24(3):387~394 |
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Net amount： 895 |
Authors： |
LIU Dong; LIN Lei |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271047), the Doctoral Programme Foundation of the Ministry of Education of China and the Shanghai Priority Academic Discipline. |
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| Abstract： |
In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic 2, which are called the variations of $G_2$. In this paper, the authors investigate their derivation algebras. It is shown that $G_2$ and its variations all possess unique nondegenerate associative forms. The authors also find some nonsingular derivations of $V_iG$ for $i=3,4,5,6,$ and thereby construct some left-symmetric structures on $V_iG$ for $i=3,4,5,6.$ Some errors about the variations of $sl(3,F)$ in [1] are corrected. |
Keywords： |
Variation, Derivation, Associative form, Left-symmetric structure |
Classification： |
17B40, 17B50 |
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