Composition algebras and cyclic p-algebras in characteristic 3

Eliyahu Matzri, Uzi Vishne

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Abstract

Given a central simple algebra A of degree 3 over a field of characteristic 3, we prove that there is a unique symmetric composition algebra extending the commutator operation on the trace-zero part modulo scalars. This is analogous to Okubo's construction of symmetric composition algebras in the case of characteristic not 3. We apply the composition algebra tools to obtain a classification of maximal 3-central spaces and maximal Galois hyperplanes of A, and prove a new common slot lemma for such algebras.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalManuscripta Mathematica
Volume143
Issue number1-2
DOIs
StatePublished - Jan 2014

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