The Bernstein Problem in Dimension 6 Original Research Article

The solution of the Bernstein problem in the regular and exceptional cases, in all dimensionsn, was made by Yu. Lyubich. A. Grishkov proved that there are no nonregular nonexceptional nuclear Bernstein algebras of type (4, 2) with stochastic realization and therefore the Bernstein problem of type (4, 2) was completely solved by the present author (J. Algebra, to appear). The aim of this paper is to describe explicitly all simplicial stochastic nonexceptional nonregular Bernstein algebras of type (3, 3). Since every nonregular nonexceptional Bernstein algebra of dimension 6 is either of type (4, 2) or of type (3, 3), the Bernstein problem in dimension 6 is completely solved in this paper.