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Simple Lie Algebras of Characteristic p with Dependent Roots
1990
Transactions of the American Mathematical Society
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We investigate finite dimensional simple Lie algebras over an algebraically closed field F of characteristic p > 7 having a Cartan subalgebra H whose roots are dependent over F . We show that H must be one-dimensional or for some root a relative to H there is a 1-section L such that the core of L is a simple Lie algebra of Cartan type H(2 : m : 4>) or W(\ : n) for some n > 1 . The results we obtain have applications to studying the local behavior of simple Lie algebras and to classifying simple
doi:10.2307/2001331
fatcat:wulip6uymnfzvaqu44dx4hwksa