ABSTRACT

Bernstein algebras appear when we try to translate the description of all stationary operators in biological heritage into algebraic language. This chapter classifies Bernstein superalgebras of dimension 4 in a similar way to the followed in dimensions 2 and 3. It is assumed that the odd part is different of zero since the case in which the odd part is zero reduces to the classification of Bernstein algebras of dimension 5, already known. By simplicity the chapter considers only the case of nonzero product. There are 30 4-dimensional Bernstein superalgebras (with odd part different of zero) nonisomorphic as Bernstein superalgebras, one for each of the 30 possible gradings.