The Bernstein Problem for Type (n−2, 2) Original Research Article

In a recent paper we solved the Bernstein problem in the nonregular nonexceptional case for the type (3, 2). The aim of this paper it is to describe explicitly all simplicial stochastic nonexceptional nonregular nonnuclear Bernstein algebras of type (n−2, 2). According to the Lyubich conjecture every nuclear Bernstein algebra with stochastic realization is regular. Consequently, this paper would completely solve the Bernstein problem for the type (n−2, 2) if the Lyubich conjecture is proved to be true.