Petersson algebra

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 .
Construction.
Suppose that "C" is a Hurwitz algebra and φ is an order 3 automorphism. Define the new product of "x" and "y" to be φ()φ2(). With this new product the algebra is called a Petersson algebra.