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- W2155796408 abstract "A Lie algebra g is said to be split graded if it is graded by a torsion free abelian group Q in such a way that the subalgebra g0 is abelian and the operators ad g0 are diagonalized by the grading. The elements of Q%{0} with gα ≠ {0} are called roots and a root α is said to be integrable if there are root vectors x± α ∈ g± α which are ad-nilpotent and generate an sl2-subalgebra g(α). In this paper we study subalgebras gΠ ⊆ g generated by the subalgebras g(α), α ∈ Π, where Π is a set of integrable roots. For |Π| ≤ 2, these subalgebras are essentially Kac–Moody algebras which permits us to generalize several results on root strings from Kac–Moody algebras to split graded algebras. A central result is the local finiteness theorem saying that whenever all roots of a split graded Lie algebra μ are integrable, then μ is locally finite. If differences of roots in Π are not roots, then Π is called a simple system. In this case we describe the structure of the subalgebras gΠ in their relationship to the corresponding Kac–Moody algebras." @default.
- W2155796408 created "2016-06-24" @default.
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- W2155796408 date "2000-03-01" @default.
- W2155796408 modified "2023-10-04" @default.
- W2155796408 title "Integrable Roots in Split Graded Lie Algebras" @default.
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- W2155796408 doi "https://doi.org/10.1006/jabr.1999.8108" @default.
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