Simple right alternative superalgebras of Abelian type whose even part is a field

Abstract

We study central simple unital right alternative superalgebras of Abelian type of arbitrary dimension whose even part is a field. We prove that every such superalgebra , except for the superalgebra , is a double, that is, the odd part can be represented in the form for a suitable . If the generating element commutes with the even part , then is isomorphic to a twisted superalgebra of vector type introduced by Shestakov [1], [2]. But if commutes with the odd part , then is isomorphic to a superalgebra introduced in [3] and called an -double. We prove that if the ground field is algebraically closed, then is isomorphic to one of the superalgebras , , .