Bernstein algebra

Summary

A Bernstein algebra is a commutative baric algebra whose weight $w$ satisfies $(x^2)^2 = w(x)^2 x^2$ for every element $x$. The identity expresses the stationarity principle of population genetics: after one generation of random mating the gene frequencies no longer change. The notion goes back to Sergei Bernstein's work of the 1920s on the Hardy–Weinberg law. Bernstein's problem asks for a classification of the inheritance laws of this kind.