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Pairing problem of generators in Kac-Moody algebras 被引量:1

Pairing problem of generators in Kac-Moody algebras
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摘要 The following result is proved: in any Kac Moody algebra g(A) , (ⅰ) given any non central element h in the Cartan subalgebra , or (ⅱ) given any real root vector x β, β∈Δ re . There exists y∈g(A) such that the subalgebra generated by y and h or y and x β contains the derived algebra g′(A) of g(A) . The following result is proved: in any Kac-Moody algebrag (A), (i) given any non-central elementh in the Cartan subalgebra h, or (ii) given any real root vectorx β, β∈Δre. There exists y ∈g(A) such that the subalgebra generated byy and h or y and xβ contains the derived algebrag′ (A) ofg(A).
出处 《Chinese Science Bulletin》 SCIE EI CAS 1998年第22期1872-1879,共8页
基金 theNationalNaturalScienceFoundationofChina(GrantNo .194 710 5 5 ) bytheNaturalScienceFoundationofBeijing
关键词 GENERATOR ROOT system REAL ROOT vector. generator root system real root vector
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同被引文献3

  • 1Kuranishi M.On everywhere clense imbeddings of free groups in Lie groups[J].Nagoya Math J.1951.2:63—71.
  • 2Lu Cai—hui.Wan Zhe—xian.On the minimal number of generators of the Lie algebras[J].J Algebra,1986,102(2):470.
  • 3Humphreys J E.lntroduction to Lie Algebras and Representation Theory[M].New York:Springer-Verlag, 1972.

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