hamilton type Lie algebras

Question

If n be positive integer and for an n-tuple of positive integers m=(m1,...,mn) then p(n,m) is graded and filtered subalgebra of W(n,m).p(n,m) is called non-alternating hamilton lie algebra over GF(2). absolute value of m equals to sum of mi for 1<=i<=m. note that 1,...,n are indices for m.

We know that p(n,m) is simple for n>=2 and N= "absolute value of" m, in addition we know that p(1,2) and p(1,1,1,1) and p(2,1,1) are simple Lie algebras over GF(2) such that their dimensions are 7,14 and 15 respectively. Would you please give me more details about mentioned lie algebras.I want to know know that how can we interpreted those kinds of lie algebras?

Answer 1

Bettina Eick has written an article "Some new simple Lie algebras in characteristic $2$" (www.icm.tu-bs.de/~beick/publ/simlie.pdf‎), with several examples and references for Hamiltonian type simple modular Lie algebras over GF(2), see the table in section $5.3$. It contains $P(1,2)$, $P(1,1,1,1)$, $P(2,1,1)$, $P(3,1)$, $P(2,2)$, etc. A further reference is L. Lin, "Nonalternating Hamiltonian algebra $P (n, m)$ of characteristic two". For interpretations of simple modular Lie algebras of Cartan type in general, see also the book(s) and survey articles of Helmut Strade.