On baric algebras with prescribed automorphisms (Q1071858)

The automorphism group of the gametic algebra for a \(2m\)-ploid population with \(n+1\) alleles is isomorphic to \(A(n)\) the affine group of \(\mathbb R^n\). This result is obtained as a special case from a study of automorphisms of slightly more general algebras. The author defines a certain class of algebras called \(\alpha\)-algebras. Roughly speaking, an \(\alpha\)-algebra is a baric algebra in which certain specified linear operators are automorphisms. The definition of these operators is too technical to be given here. The author classifies the \(\alpha\)-algebras for \(m\leq 5\). In a later section he has some results also in the case where \(m>5\). Finally, he claims to have results dealing with derivations of \(\alpha\)-algebras which he says will be published elsewhere.