parabolic element of PSL(2,ℤ)
C51328
concept
A parabolic element of PSL(2,ℤ) is a Möbius transformation represented by an integer 2×2 matrix of determinant 1 with trace ±2, which fixes exactly one point on the extended real line (typically a rational cusp) and acts there by translation.
All labels observed (1)
| Label | Occurrences |
|---|---|
| parabolic element of PSL(2,ℤ) canonical | 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: parabolic element of PSL(2,ℤ)
Generated description
A parabolic element of PSL(2,ℤ) is a Möbius transformation represented by an integer 2×2 matrix of determinant 1 with trace ±2, which fixes exactly one point on the extended real line (typically a rational cusp) and acts there by translation.
Instances (1)
| Instance | Via concept surface |
|---|---|
|
T:z ↦ z+1
surface form:
T : z ↦ z + 1
|
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