Automorphisms of simple Lie algebras G(n) Over GF(2)

Abstract

We define certain algebras ℭ(n) over a commutative ring K based on the combinatorics of n dots. If K is a field of characteristic 2, then ℭ(n) decomposes as G(n) ⊗𝔽₂K where G(n) belongs the infinite sequence of simple Lie algebras over the field 𝔽₂ that was introduced by Kaplansky in 1982. We show that Aut(ℭ(n)) is isomorphic to {±1} × 𝔖_n for n > 4.

Key Words:

• Combinatorial algebra
• Linear algebra
• Lie algebra
• Matrix rank

2010 Mathematics Subject Classification:

• 05E15
• 15A03
• 17B40