On simple reducible depth-two Lie algebras with classical reductive null component
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- by Thomas B. Gregory PDF
- Proc. Amer. Math. Soc. 85 (1982), 318-322 Request permission
Abstract:
We classify the simple finite-dimensional reducible graded Lie algebras of the form ${L_{ - 2}} \oplus {L_{ - 1}} \oplus {L_0} \oplus {L_1} \oplus \cdots \oplus {L_k}$ over an algebraically closed field of characteristic greater than 3, where ${L_0}$ is reductive and classical such that no nonzero element of the center of ${L_0}$ annihilates ${L_{ - 2}}$ and where ${L_{ - 1}}$ is the sum of two proper ${L_0}$-submodules.References
- Thomas B. Gregory, A characterization of the contact Lie algebras, Proc. Amer. Math. Soc. 82 (1981), no. 4, 505–511. MR 614868, DOI 10.1090/S0002-9939-1981-0614868-5
- Thomas B. Gregory, On simple reducible Lie algebras of depth two, Proc. Amer. Math. Soc. 83 (1981), no. 1, 31–35. MR 619975, DOI 10.1090/S0002-9939-1981-0619975-9
- Thomas B. Gregory, Simple Lie algebras with classical reductive null component, J. Algebra 63 (1980), no. 2, 484–493. MR 570725, DOI 10.1016/0021-8693(80)90085-X
- 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 (Russian). MR 0276286
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 318-322
- MSC: Primary 17B20; Secondary 17B50
- DOI: https://doi.org/10.1090/S0002-9939-1982-0656092-7
- MathSciNet review: 656092