Classification of finite-dimensional Lie algebras over a field of characteristic 2 is a widely open problem. We will discuss a certain 15-dimensional such algebra, first appearing in the works of Skryabin. It possesses a number of interesting properties which may be typical for a certain class of simple Lie algebras, and may help to tame a currently wild zoo of characteristic 2 examples. (Based on joint work with Alexander Grishkov, Henrique Guzzo Jr., and Marina Rasskazova).
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