In mathematics, a Petersson algebra is a composition algebra over a field constructed from an order-3 automorphism of a Hurwitz algebra. They were first constructed by .
Suppose that C is a Hurwitz algebra and ÃÂ is an automorphism of order 3. Define the new product of x and y to be ÃÂ()ÃÂ<sup>2</sup>(). With this new product the algebra is called a Petersson algebra.