# Contents

## Definition

For $S:C\to {𝔸}^{1}$ an action functional, the $𝒪\left(C\right)$-module of its Noether identities is the kernel ${N}_{S}↪\mathrm{Der}\left(𝒪\left(C\right)\right)$ of the canonical morphism

${\iota }_{dS}:\mathrm{Der}\left(𝒪\left(S\right)\right)\to 𝒪\left(S\right)\phantom{\rule{thinmathspace}{0ex}}.$\iota_{d S} : Der(\mathcal{O}(S)) \to \mathcal{O}(S) \,.

See BRST-BV complex for background and details.

## Examples

Assume that $C$ is sufficiently well behaved and of finite dimension such that the module of derivations has (locally) a basis $\left\{{\partial }_{i}{\right\}}_{i}$. Then the Noether identities are (locally) tuples of functions $\left\{{v}^{i}\right\}$ such that

$\sum _{i}{v}^{i}{\partial }_{i}S=0\phantom{\rule{thinmathspace}{0ex}}.$\sum_i v^i \partial_i S = 0 \,.
Created on March 8, 2011 14:13:44 by Urs Schreiber (131.211.232.88)