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Irreducible Lie algebras of infinite type


Author: Robert Lee Wilson
Journal: Proc. Amer. Math. Soc. 29 (1971), 243-249
MSC: Primary 17.30
DOI: https://doi.org/10.1090/S0002-9939-1971-0277582-8
MathSciNet review: 0277582
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Abstract: Let V be a finite dimensional vector space over an algebraically closed field of characteristic $ \ne 2,3,5$. It is shown that if $ L \subseteq {\text{gl}}(V)$ is an irreducible Lie algebra of infinite type then either $ V = 2r \geqq 4$ and $ L = {\text{sp}}(V),\dim \,V = 2r \geqq 4$ and $ L = {\text{csp}}(V)$, or there exists $ A \in L$ such that $ A \ne 0 = {({\text{ad}}\;A)^2}$. As a corollary we obtain E. Cartan's classification of the irreducible Lie algebras of infinite type over C.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0277582-8
Keywords: Cartan prolongation, infinite Lie algebra of Cartan type
Article copyright: © Copyright 1971 American Mathematical Society

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