A sufficient condition for pairing problem of generators in symmetrizable Kac–Moody algebras

✍ Scribed by Caihui Lu; Haixia Xu

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 92 KB
• Volume: 260
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00051-6

✦ Synopsis

In a symmetrizable Kac-Moody algebra g(A), let α = n i=1 k i α i be an imaginary root satisfying k i > 0 and α, α ∨ i < 0 for i = 1, 2, . . . , n. In this paper, it is proved that for any x α ∈ g α \ {0}, satisfying [x α , f n ] = 0 and [x α , f i ] = 0 for i = 1, 2, . . . , n -1, there exists a vector y such that the subalgebra generated by x α and y contains g (A), the derived subalgebra of g(A).