even unimodular lattice
C22011
concept
An even unimodular lattice is a free abelian group of finite rank equipped with a positive-definite symmetric bilinear form whose Gram matrix has determinant 1 and for which the squared length of every lattice vector is an even integer.
All labels observed (3)
| Label | Occurrences |
|---|---|
| even unimodular lattice canonical | 3 |
| integral lattice | 1 |
| positive-definite lattice | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: even unimodular lattice
Generated description
An even unimodular lattice is a free abelian group of finite rank equipped with a positive-definite symmetric bilinear form whose Gram matrix has determinant 1 and for which the squared length of every lattice vector is an even integer.
Instances (3)
| Instance | Via concept surface |
|---|---|
| Leech lattice | — |
|
John Leech
surface form:
Leech lattice
|
— |
| E8 lattice | — |