Classification of bernstein algebras of type (3, n - 3)

A classification of Bernstein algebras in dimensions n ? 4 has been made by Holgate in 2], however that article contains no classification up to isomorphism, the problem is solved by Lyubich in 4] when K = R or C, and by Cortes 1] in the general case. Also Lyubich has given in 5] a classification of the regular nonexceptional Bernstein algebra of type (3,n?3) and a classification but not up to isomorphism of nonregular nonexceptional Bernstein algebras of type (3,n ? 3) when K = C. The aim of this paper it to characterize, up to isomorphism, Bernstein algebras of type(2, n ? 2) and nonexceptional of type(3, n ?3) over a infinite commutative field K whose characteristic is different from 2.