In this book, we introduce a new type of algebra, which we call evolution algebras. These are algebras in which the multiplication tables are of a special type. They are motivated by evolution laws of genetics. We view alleles (or organelles or cells, etc,) as generators of algebras. Therefore we define the multiplication of two “alleles” Gi and Gj by Gi · Gj = 0 if i = j. However, Gi ·Gi is viewed as “self-reproduction,” so that Gi ·Gi = j pijGj, where the summation is taken over all generators Gj . Thus, reproduction in genetics is represented by multiplication in algebra
