Commuting variety of Witt algebra.

Let g=W1 be the Witt algebra over an algebraically closed field k of characteristic p > 3; and let be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250: 473-484], we show that the variety is reducible, and not equidimensional. Irreducible components of and their dimensions are precisely given. As a consequence, the variety is not normal. [ABSTRACT FROM AUTHOR]