A historical perspective of Tian’s evolution algebras

Two-dimensional perfect evolution algebras over domains

“…For instance, consider the group lim →2 D × /(D × ) [3] . Since 2 and 3 are coprime, the transition homomorphisms (•) 2 are isomorphisms.…”

“…In [2], the classification of the evolution algebras of dimension two over arbitrary fields is provided. In [3], we can find more information about the evolution of the research in the field of evolution algebras defined in [10]. Our contribution in this work is the study of two-dimensional perfect evolution algebras over domains.…”

On $\exp(Der(E))$ of nilpotent evolution algebras

“…Evolution algebras allowed introduce useful algebraic techniques and methods into the investigation of some digraphs because such kind of algebras and weighted digraphs can be canonically identified [13,28] However, a full classification of nilpotent evolution algebras is far from its solution. For review on recent development on evolution algebras, we refer the reader to [11].…”

Tensor product of finite dimensional nilpotent evolution algebras

“…Later on, evolution algebras are used to model non-Mendelian genetics laws [9][10][11][12][13]. Moreover, these algebras are tightly connected with group theory, the theory of knots, dynamic systems, Markov processes, and graph theory [14][15][16][17][18] and [43,44,46]. Evolution algebras introduced proper algebraic techniques and methods for investigating some digraphs because such algebras and weighted digraphs can be canonically identified [7,19].…”