EXISTENCE OF 2-EXCEPTIONAL BERNSTEIN ALGEBRAS

Abstract

Given a Bernstein algebraA = Fe⊕U ⊕V , the two ordered pairs of integers (1 + dimU,dimV ) and (dim(UV + V 2),dimU2) are called, respectively, the type and the subtype of A. In this paper we determine the minimum and the maximum dimension of the subspace UV+V 2 in 2-exceptional Bernstein algebras (those satisfying U(UV)=0 and U((UV)V ) = 0) and we introduce an algorithm to construct 2exceptional Bernstein algebras for some types and subtypes.