Simple Lie Algebras and Graphs Original Research Article

Kaplansky introduced several classes of central simple Lie algebras in characteristic 2. We view these algebras in terms of graphs, and we classify them using a theorem of Shult characterizing graphs with the "cotriangle condition"; there is also a connection with Fischer′s theorem on groups generated by 3-transpositions. Uniqueness of these algebras is phrased in terms of their cohomology, and a lower bound for dim H1 of these algebras is given.