Flexible algebras of degree two

Mayne, Joseph H.

doi:10.1090/S0002-9947-1972-0311727-1

Flexible algebras of degree two
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Trans. Amer. Math. Soc. 172 (1972), 69-81 Request permission

Abstract:

All known examples of simple flexible power-associative algebras of degree two are either commutative or noncommutative Jordan. In this paper we construct an algebra which is partially stable but not commutative and not a noncommutative Jordan algebra. We then investigate the multiplicative structure of those algebras which are partially stable over an algebraically closed field of characteristic $p \ne 2,3,5$. The results obtained are then used to develop conditions under which such algebras must be commutative.

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