nLab integral lattice

Idea

A lattice in an inner product space is called integral if the inner product of pairs of lattice vectors takes values in the integer numbers.

Integral lattices may encode higher structures, such as braided 2-groups (Baez 2015) and multiplicative bundle gerbes (Ganter 2014).

Related concepts

• unimodular integral lattice

• modular integral lattice

References

Lecture notes:

• Andries E. Brouwer, Lattices, Course notes (2002) [pdf, pdf]

Discussion of related higher structures:

• John Baez. Integral octonions part 12 (url).

• Nora Ganter. Categorical Tori, SIGMA 14 014 (2018) [arXiv:1406.7046, doi:10.3842/SIGMA.2018.014]