---
date: 2022-02-23 18:45
modification date: Thursday 24th March 2022 14:59:49
title: smooth algebra
aliases: [smooth algebra]

---

Last modified date: <%+ tp.file.last_modified_date() %>


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

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# smooth algebra

A definition due to Kontsevich: a [DGA](Unsorted/DGA.md) $A$ is **smooth** if $A \in \Perf\left(A \otimes A^{\op} \right)$. It is compact if $\operatorname{dim} H^{\bullet}(A, d)<\infty$. This properties are preserved under the derived [[Morita equivalence]].

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\begin{tikzcd}
	&&&& P \\
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![Pasted image 20210625203016](attachments/Pasted%20image%2020210625203016.png)

![](attachments/Pasted%20image%2020220324150009.png)