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OALib Journal期刊
ISSN: 2333-9721
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李代数的张量积所确定的Leibniz代数
, PP. 93-102
Keywords: Leibniz代数&searchField=keyword">Leibniz代数')"href="#">Leibniz代数,不变对称双线性型,张量积,导子,边染色,最大度,第一类图
Abstract:
讨论了李代数\,$\mathcal{G}$\,以及由这个李代数诱导的\$\mathrm{Leibniz}$\,代数\,$\mathcal{G}\otimes\mathcal{G}$\,的一些性质,主要从不变双线性型和导子看这两个代数之间的差异,证明了在特定条件下两者的不变双线性型维数是一致的.为进一步确定李代数\,$\mathcal{G}$\,和\,$\mathcal{G}\otimes\mathcal{G}$\的差异,讨论了由\,$\mathcal{G}\otimes\mathcal{G}$\,诱导的一类重要的李代数\,$\mathcal{G}\boxtimes\mathcal{G}$;最后证明了,如果\,$\mathcal{G}$\,是有限维半单李代数,$\mathcal{G}$\,和\,$\mathcal{G}\boxtimes\mathcal{G}$\,是同构的.
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