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Corrections to the paper of B. Yu. Weisfeiler and V. G. Kac “Exponentials in Lie algebras of characteristic $$p$$”. (English. Russian original) Zbl 0929.17023
Russ. Acad. Sci., Izv., Math. 45, No. 1, 229 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 4, 224 (1994).
From the text: “In the formulation of Theorem 3.7 we omitted the Lie algebra of characteristic 3 having rank 3 and dimension 29. It has two structures of a contragradient Lie algebra; they correspond to the Cartan matrices $\left(\begin{matrix} \r&\quad\r&\quad\r\\ 2 & -1 & 0\\ -1 & 2 & -1\\ 0 & -1 & 0\end{matrix} \right)\quad \text{and}\quad\left(\begin{matrix} \r&\quad\r&\quad\r\\ 2 & -1 & 0\\ -2 & 2 & -1\\ 0 & -1 & 0\end{matrix}\right).$ These matrices should be added to the formulation of Lemma 3.10. There are no other finite-dimensional simple contragradient Lie algebras of characteristic 3. This Lie algebra was constructed by G. Brown [Math. Ann. 261, 487-492 (1982; Zbl 0485.17005)], and S. M. Skryabin [Mat. Sb. 183, No. 8, 3-22 (1992; Zbl 0849.17020)] proved that it has the structure of a contragradient Lie algebra (these papers were brought to my attention by A. I. Kostrikin)”.

MSC:
 17B50 Modular Lie (super)algebras
Keywords:
modular Lie algebras; exponentials
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