English

Classification in chains of three-dimensional real evolution algebras

Rings and Algebras 2021-07-07 v1 Commutative Algebra

Abstract

A chain of evolution algebras (CEA) is an uncountable family (depending on time) of evolution algebras on the field of real numbers. The matrix of structural constants of a CEA satisfies Kolmogorov-Chapman equation. In this paper, we consider three CEAs of three-dimensional real evolution algebras. These CEAs depend on several (non-zero) functions defined on the set of time. For each chain we give full classification (up to isomorphism) of the algebras depending on the time-parameter. We find concrete functions ensuring that the corresponding CEA contains all possible three-dimensional evolution algebras.

Cite

@article{arxiv.2107.02756,
  title  = {Classification in chains of three-dimensional real evolution algebras},
  author = {Bobomurad Narkuziyev and Utkir Rozikov},
  journal= {arXiv preprint arXiv:2107.02756},
  year   = {2021}
}

Comments

34 pages, 3 figures

R2 v1 2026-06-24T03:56:26.183Z