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arXiv · 2104.04177

Embedding theory of lattices and its application for $2$-integrable lattices

Qianqian Yang·Kiyoto Yoshino
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Abstract

For a positive integer $s$, a lattice $L$ is said to be $s$-integrable if $\sqrt{s}\cdot L$ is isometric to a sublattice of $\mathbb{Z}^n$ for some integer $n$. Conway and Sloane found two minimal non $2$-integrable lattices of rank $12$ and determinant $7$ in 1989. We find two more ones of rank $12$ and determinant $15$. Then we introduce a method of embedding a given lattice into a unimodular lattice, which plays a key role in proving minimality of non $2$-integrable lattices and finding candidates for non $2$-integrable lattices.

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Qianqian Yang, Kiyoto Yoshino. 2021-04-09. Embedding theory of lattices and its application for $2$-integrable lattices. https://arxiv.org/abs/2104.04177

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