# nLab star product

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Idea

In deformation quantization of Poisson manifolds the commutative product $\cdot$ of the commutative algebra of functions is replaced by a noncommutative associative product. This is often called a star product and denoted “$\star$”.

An archetypical example is the Moyal star product that deforms the function algebra on a Poisson vector space, and sometimes “star product” is by default understood to be a Moyal star product.

More recently also nonassociative “star products” have been proposed to be of interest.

Revised on April 2, 2013 20:17:51 by Urs Schreiber (131.174.41.18)