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($\overline{x}$)φ2($\overline{y}$). With this new product the algebra is called a Petersson algebra.