---
created: 2022-03-27T00:52
updated: 2023-04-03T09:44
title: "deformation theory is controlled by dg Lie algebras"
aliases: [deformation theory is controlled by dg Lie algebras, deforming an algebra, deformation of an algebra]
---


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- Tags 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# deformation theory is controlled by dg Lie algebras

![](attachments/2023-03-31-6.png)

## Using the Gerstenhaber bracket

![](2023-03-31-65.png)
![](2023-03-31-66.png)


# Defining formal deformations of an algebra

![](2023-03-31-93.png)

## Higher corrections to associativity

![](2023-03-31-97.png)
![](2023-03-31-98.png)
![](2023-03-31-99.png)

## Multiparameter deformations

![](2023-04-03.png)