alternating form
C27995
concept
An alternating form is a multilinear map on a vector space that changes sign whenever two of its arguments are swapped, and hence vanishes whenever any two arguments are equal.
All labels observed (5)
| Label | Occurrences |
|---|---|
| differential 1-form | 2 |
| Kähler form | 1 |
| alternating form canonical | 1 |
| antisymmetric tensor | 1 |
| real differential form | 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: alternating form
Generated description
An alternating form is a multilinear map on a vector space that changes sign whenever two of its arguments are swapped, and hence vanishes whenever any two arguments are equal.
Instances (5)
| Instance | Via concept surface |
|---|---|
| Weil pairing | — |
| Levi-Civita symbol | antisymmetric tensor |
| Pfaffian form | differential 1-form |
| Maurer–Cartan form | differential 1-form |
| Fubini–Study form | Kähler form |