TOPICS
Search

Modular Euclidean Lattice

A modular Euclidean lattice, also called an l-modular lattice, is an integral point lattice Lambda subset R^n that is isometric to sqrt(l)Lambda^*, where l is a positive integer and

Lambda^*={x in R^n:<x,y> in Z for every y in Lambda},

is the dual lattice (Quebbemann 1995). The case l=1 gives the unimodular lattices. The 16-dimensional Barnes-Wall lattice is 2-modular, while the 12-dimensional Coxeter-Todd lattice is 3-modular (Choie and Solé 2008).

This use of the term "modular lattice" is unrelated to the order-theoretic modular lattice, which is defined by the modular identity.

See also

Barnes-Wall Lattice, Coxeter-Todd Lattice, Modular Lattice, Point Lattice

Explore with Wolfram|Alpha

References

Choie, Y.-J. and Solé, P. "Broué-Enguehard Maps and Atkin-Lehner Involutions." Eur. J. Combin. 29, 24-34, 2008. https://doi.org/10.1016/j.ejc.2007.01.004.Quebbemann, H.-G. "Modular Lattices in Euclidean Spaces." J. Number Th. 54, 190-202, 1995. https://doi.org/10.1006/jnth.1995.1111.

Cite this as:

Weisstein, Eric W. "Modular Euclidean Lattice." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ModularEuclideanLattice.html

Subject classifications