Quartic trace identity for exceptional Lie algebras
Quartic trace identity for exceptional Lie algebras
复制标题
特殊李代数的四次迹恒等式
DOI：
10.1063/1.524127
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发表时间：
1979
影响因子：
1.3
通讯作者：
S. Okubo
中科院分区：
文献类型：
--
作者：
S. Okubo
设X是简单李代数的一般不可约表示{λ}中的一般元X的表示矩阵。然后，对于所有例外李代数以及A1和A2，我们证明了四次迹恒等式Tr(X4) =K (λ)[Tr(X2)]2的有效性，其中常数K （λ）仅依赖于不可约表示{λ}，并计算了其显式形式。讨论了二阶和四阶指标的一些应用。
Let X be a representation matrix of generic element x of a simple Lie algebra in generic irreducible representation {λ} of the Lie algebra. Then, for all exceptional Lie algebras as well as A1 and A2, we can prove the validity of a quartic trace identity Tr(X4) =K (λ)[Tr(X2)]2, where the constant K (λ) depends only upon the irreducible representation {λ}, and its explicit form is calculated. Some applications of second and fourth order indices have also been discussed.