Abstract
The Lie algebra comes from P. Deligne’s work on the exceptional series of Lie groups. Using the triality algebra, J. Landsberg and L. Manivel construct this Lie algebra in 2006. In this paper, we study the structure of following B. Gross and N. Wallach’s work on the highest root and Heisenberg parabolic subalgebra. The process of removing the lowest root from the extended Dynkin diagram of will contribute to the components of . We also study the branching rule of to and . We use the computer algebra system SageMath to carry out the branching rule calculations. Then we calculate the Dynkin indices for . We find that the number 24 behaves like the ‘dual Coxeter number’ of .
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