In Chapters 1-4 we describe the automorphism group of an arbitrary member, T(n), from an infinite family of Lie algebras defined over the two element field, GF(2). The algebra T (n) has a vector space basis consisting of the edges and vertices of the complete graph on n vertices, while the Lie bracket on T(n) is defined to encode the incidence relation of the graph. The main result is that, when n ≠ 3, the automorphism group of T(n ) is isomorphic to the group of affine transformations of n-dimensional space over GF(2) which can be written in the form d + Px with P orthogonal.;In Chapter 5 we establish that the 14-dimensional simple Bi-Zassenhaus algebra B(2; 1) is not isomorphic to the 14-dimensional simple algebra G(4) discovered by Kaplansky, thereby answering a question of Jurman.
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