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 automorphism of order 3. 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, vol. 44, Providence, RI: American Mathematical Society, ISBN   0-8218-0904-0, Zbl   0955.16001
• Petersson, Holger P. (1969), "Eine Identität fünften Grades, der gewisse Isotope von Kompositions-Algebren genügen", Math. Z. (in German), 109 (3): 217–238, doi:10.1007/BF01111407, MR   0242910, S2CID   122353090