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 Petersson (1969).
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(x)φ2(y). With this new product the algebra is called a Petersson algebra.
References
Petersson algebra Wikipedia(Text) CC BY-SA