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 {{harvtxt|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({{overline|x}})φ2({{overline|y}}). With this new product the algebra is called a Petersson algebra.
References
- {{citation | last1=Knus | first1=Max-Albert | last2=Merkurjev | first2=Alexander | author2-link=Alexander Merkurjev | last3=Rost | first3=Markus | author3-link=Markus Rost | last4=Tignol | first4=Jean-Pierre | author-link4=Jean-Pierre Tignol | title=The book of involutions | zbl=0955.16001 | series=Colloquium Publications | publisher=American Mathematical Society | volume=44 | location=Providence, RI | year=1998 | isbn=0-8218-0904-0 }}
- {{citation|mr=0242910
|last=Petersson|first= Holger P.
|title=Eine Identität fünften Grades, der gewisse Isotope von Kompositions-Algebren genügen|language=German
|journal=Math. Z. |volume=109|year= 1969|issue=3 |pages= 217–238|doi=10.1007/BF01111407|s2cid=122353090}}
Category:Non-associative algebras
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