Algebraically Generated Superalgebras

Abstract

A simple right-alternative superalgebra whose even part has zeromultiplication is called singular.In the paper, finite-dimensional algebraically generated singular superalgebraswith non-degenerate switch are introduced and studied.A special case of such algebras, namely, linearly generated superalgebras,was previously classified by the authors.The construction of the extended double is given in the paper and it is provedthat an algebraically generated singular superalgebra with non-degenerateswitch is an extended double.It is also shown that, for any number $d\geq32$, there exists a d-dimensionalextended double.