An Algorithm for constructing Hjelmslev planes

Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations of projective planes and affine planes. We present an algorithm for constructing a projective Hjelmslev planes and affine Hjelsmelv planes using projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv planes can be constructed in this way. As a corollary it is shown that all 2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014, Springer Proceedings in Mathematics & Statistics 13

Modular Lie algebras and the Gelfand-Kirillov conjecture

Let g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G_2.Comment: 20 page

A note on the Campbell-Hausdorff formula

In his book (“Lie Algebras,” Interscience, 1962) Jacobson proves the Campbell-Hausdorff formula for formal power series in Lie algebras. In this short note we shall prove it for finite-dimensional Lie groups making use of parts of Jacobson's proof