Sums of Isometric Pairs of Lattices

TL;DR

This paper explores a method for constructing new lattices by summing pairs of isometric lattices, providing general results and examples involving well-known small-rank lattices.

Contribution

Introduces a novel lattice construction technique based on summing isometric pairs, with theoretical results and illustrative examples.

Findings

Established general properties of the sum construction

Provided examples with well-known small-rank lattices

Demonstrated the method's applicability to various lattice types

Abstract

This paper is an investigation of a procedure for constructing lattices by means of taking the sum of a pair of isometric lattices. We present various general results pertaining to this construction and discuss several examples of it applied to various well-known lattices of small rank.