Defining a cocycle

asked 2023-10-15 20:23:25 +0200

asdfg gravatar image

updated 2024-04-25 10:45:50 +0200

FrédéricC gravatar image

Hello everyone,

I would like to define an arbitrary group cocycle. That is, I want to define a function $f:A\times A\to \mathbb{T}$, where $A$ is my group and $\mathbb{T}$ is the unit circle, such that $f$ satisfies the following rule:

$f(a,b)f(ab,c) = f(b,c)f(a,bc) \quad\forall a,b,c\in A.$

Any help will be appreciated it.

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The given property does not uniquely define the function, and so your question is unclear.

Max Alekseyev gravatar imageMax Alekseyev ( 2023-10-15 22:31:26 +0200 )edit

Can you provide some Sage-specific details? What have you tried so far?

John Palmieri gravatar imageJohn Palmieri ( 2023-10-16 02:47:42 +0200 )edit