The Irreducible Tensor Bases of Exceptional Lie Algebras 1. G2, F_4 and E_6
Dong Ruan (1), Hongzhou Sun (1), QiZhi Han (2) ((1) Tsinghua, University (Beijing), (2) Peking University (Beijing))
TL;DR
This paper constructs explicit irreducible tensor bases for the exceptional Lie algebras G2, F4, and E6 by organizing their Cartan-Weyl bases along specific subgroup chains, providing detailed commutation relations.
Contribution
It introduces explicit irreducible tensor bases for G2, F4, and E6, along with their commutation relations, enhancing understanding of their algebraic structure.
Findings
Explicit tensor bases for G2, F4, and E6 are constructed.
Commutation relations for these bases are explicitly provided.
The bases are organized according to specific subgroup chains.
Abstract
The irreducible tensor bases of exceptional Lie algebras G2, F4 and E6 are built by grouping their Cartan-Weyl bases according to the respective chains G2> SO(3) * SO(3), F4 > SO(3)*SO(3)*SO(3)*SO(3) and E6> SO(3)*SO(3)*SO(3)*SO(3). The explicit commutation relations of the irreducible tensor bases of these algebras are given also respectively.
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Taxonomy
TopicsAdvanced Topics in Algebra · Nonlinear Waves and Solitons · Carbohydrate Chemistry and Synthesis