The Irreducible Tensor Bases of Exceptional Lie Algebras 1. G2, F₄ and E₆

2001/11/01 by Dong Ruan, Ruan, Dong, Hongzhou Sun +3
Mathematics · Physics and Astronomy · #17B10 #17B25 #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #math-ph #math.GR #math.MP #msc:17B10 #msc:17B25

paper · pdf · doi:10.48550/arxiv.math-ph/0111003

19 Pages, LaTex

arxiv created 2001/11/01 · arxiv updated 2009/11/30

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.

Related

• The exceptional series through the fifth tensor power
• The Structure Constants of the Exceptional Lie Algebra \mathfrak g₂ in the Cartan-Weyl Basis
• Series of Lie Groups
• Linear models of the exceptional Lie algebra \mathfrake₈
• Tensor powers of adjoint representations ot classical Lie groups