title: Petersson algebra
text: # 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 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 $φ(x)φ^2(y).$ With this new product the algebra is called a Petersson algebra.
  
  