Nilpotent variety of restricted Lie algebra.

Cong Chen

Frank Adams 2,

In 1990, Premet conjectured that for any finite dimensional restricted Lie algebra \(L\) over an algebraically closed field \(k\), the nilpotent variety \(N(L)\) is irreducible. In this talk, I will verify this conjecture for \(L=sl_{2}\otimes O_{1}+kd/dx\), but I will start with basic theory of modular Lie algebras and state some Premet's results on \(N(L)\).

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