Namespaces
Variants
Actions

Unimodular lattice

From Encyclopedia of Mathematics
Revision as of 08:27, 6 June 2020 by Ulf Rehmann (talk | contribs) (tex encoded by computer)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search


A lattice $ L $ in $ \mathbf R ^ {n} $ such that $ \mathop{\rm vol} ( \mathbf R ^ {n} \mid L) = 1 $. If $ a _ {1} \dots a _ {n} $ are $ n $ vectors in $ \mathbf R ^ {n} $, then the lattice spanned by $ a _ {1} \dots a _ {n} $ is unimodular if and only if $ | \mathop{\rm det} ( a _ {1} \dots a _ {n} ) | = 1 $( because $ \mathop{\rm vol} ( \mathbf R ^ {n} \mid L ( a _ {1} \dots a _ {n} )) = | \mathop{\rm det} ( a _ {1} \dots a _ {n} ) | $).

References

[a1] J. Milnor, D. Husemoller, "Symmetric bilinear forms" , Springer (1973) pp. 16
How to Cite This Entry:
Unimodular lattice. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unimodular_lattice&oldid=49078