Superalgebras and algebras with involution: classifying varieties of quadratic growth

Abstract

Let be a field of characteristic zero. By a -algebra we mean a superalgebra or an algebra with involution over In the last years, the sequence of -codimensions of a -algebra has been extensively studied. In this paper, we classify varieties generated by unitary -algebras having quadratic growth of -codimensions. As a consequence we obtain that a unitary -algebra with quadratic growth is -equivalent to a finite direct sum of minimal unitary -algebras with at most quadratic growth of the -codimensions. In addition, we explicit all quadratic functions describing the -codimension sequence of a unitary -algebra.