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)φ²(y). With this new product the algebra is called a Petersson algebra.

References

• Knus, Max-Albert; Merkurjev, Alexander; Rost, Markus; Tignol, Jean-Pierre (1998), The book of involutions, Colloquium Publications, 44, Providence, RI: American Mathematical Society, ISBN 0-8218-0904-0 
• Petersson, Holger P. (1969), "Eine Identität fünften Grades, der gewisse Isotope von Kompositions-Algebren genügen" (in German), Math. Z. 109: 217–238, doi:10.1007/BF01111407