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Proceedings of the American Mathematical Society

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On simple reducible Lie algebras of depth two

Author: Thomas B. Gregory
Journal: Proc. Amer. Math. Soc. 83 (1981), 31-35
MSC: Primary 17B20; Secondary 17B70
MathSciNet review: 619975
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Abstract: We show that under certain circumstances simple finite-dimensional reducible graded Lie algebras of the form $ {L_{ - 2}} \oplus {L_{ - 1}} \oplus {L_0} \oplus {L_1} \oplus \cdots \oplus {L_k}$ can be given irreducible transitive gradations of the form $ {M_{ - 1}} \oplus {M_0} \oplus \cdots \oplus {M_{[k/2]}}$.

References [Enhancements On Off] (What's this?)

  • [1] T. B. Gregory, A characterization of the contact Lie algebras, Proc. Amer. Math. Soc. (to appear). MR 614868 (83e:17012)
  • [2] -, Simple Lie algebras with classical reductive null component, J. Algebra 63 (1980), 484-493. MR 570725 (81h:17015)
  • [3] V. G. Kac, The classification of the simple Lie algebras over a field with non-zero characteristic, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 385-408; English transl., Math. USSR Izv. 4 (1970), 391-413. MR 0276286 (43:2033)

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