Non-alternating hamiltonian algebraP(n,m)of characteristic two

Abstract

Over a field F of characteristic p = 2, a class of Lie algebras P(n,m), called non-alternating Hamiltonian algebras, is constructed, where n is a Positive integer and m=(m1, ⋯,mn) is an n-tuple of positive integers. P(n,m) is a graded and filtered subalgebra of the generalized Jacobson-Witt algebra W(n,m) and bears resemblance to the Lie algebras of Cartan type. P(n,m) is shown to be simple unless m=1 and n < 4. The dimension of P(n,m) is Different from the Lie algebras of Cartan type, all P(n,m) are nonrestrictable. The derivation algebra of P(n,m) is determined, and the natural filtration of P(n,m) is proved to be invariant. It is then determined that P(n,m) is a new class of simple Lie algebras if (n,m) satisfies some condition.