---
created: 2022-03-27 00:04
updated: 2023-04-02T13:00
title: "Gerstenhaber bracket"
aliases: [Gerstenhaber algebra, BV algebra]
---

---

- Tags 
	- #todo/untagged
- Refs:
	- BV structure on [symplectic cohomology](symplectic%20cohomology): <https://arxiv.org/pdf/0704.2055.pdf#page=1&zoom=auto,-200,55>
- Links:
	- [little discs operad](little%20discs%20operad)
	- [deformation quantization](deformation%20quantization.md)

---

# Gerstenhaber bracket

Example: $\HoH(\cat{A}, \cat{A})$ for $\cat A = \Fuk(M)$ an $A_\infty$ category is a Gerstenhaber algebra, and the [symplectic cohomology](symplectic%20cohomology) $\mathrm{SH}(\cat M)$ carries a BV algebra structure.

![](attachments/Pasted%20image%2020220327000501.png)
![](attachments/Pasted%20image%2020220327000514.png)