On Right Alternative Superalgebras

Abstract

Simple right alternative superalgebras which have a simple algebra as even part and, as odd part, an irreducible bimodule over the even part are investigated. Under these conditions, superalgebras with one dimensional even part are classified, as well as superalgebras having M ₂(F) as even part and a unital irreducible bimodule over M ₂(F) of dimension less than or equal to 6 as odd part. It is shown that there is only a unique non alternative simple right alternative superalgebra of the first type and, for the second type, there is a infinite family depending on a single parameter.

Key Words:

• Bimodules
• Right alternative algebras
• Superalgebras

2010 Mathematics Subject Classification:

• 17A70
• 17D15

Notes

Communicated by A. Elduque