Lattice packings through division algebras (Q2106543)

A lattice is a discrete closed subset \(\Lambda\) of a real vector space \(V\) with finite dimension with the property that \(V/\Lambda\) has finite volume. A lattice packing is a collection of balls of a given radius centered at the lattice points with the property that distinct balls are disjoint. The author gives a construction of lattice packings in a family of dimensions using division algebras generalizing a previously known construction. This generalization uses probabilistic methods to find these packings in certain dimensions with good packing densities improving known lower bounds in some cases and uses a division algebra variant of Siegel's mean value theorem.