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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
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