mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, a Petersson algebra is a

composition algebra In mathematics, a composition algebra over a field is a not necessarily associative algebra over together with a nondegenerate quadratic form that satisfies :N(xy) = N(x)N(y) for all and in . A composition algebra includes an involution ...

over a field constructed from an order-3

automorphism In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all 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.

References

* * Composition algebras Non-associative algebras {{abstract-algebra-stub