---
date: 2022-03-23
tags: [web/quick_notes]
---

# 2022-03-23

## 15:22

#personal/idle-thoughts 

A [DGA](DGA.md) has a multiplication like
\[
xy = (-1)^{\abs x \abs y} yx
.\]
What if you replaced this with some kind of $p\dash$graded condition instead?
Note that $\ts{\pm 1} = \mu_2$, so maybe define a character $\chi_2: A\tensorpower{k}{2} \to \mu_2$ to rewrite this as 
\[
xy = \chi_2(x, y) yx
.\]
More generally, could you define something like $\chi_p: A\tensorpower{k}{2} \to \mu_p$?

> Super super vague!
> Inspired by the idea that certain maps $f$ between DGAs don't commute with differentials, so aren't DGA morphisms, but do satisfy $\bd f(\omega) = p f(\bd \omega)$ instead. See [p-derivation](p-derivation)?