English

On evolution algebras

Commutative Algebra 2010-04-08 v1

Abstract

The structural constants of an evolution algebra is given by a quadratic matrix AA. In this work we establish equivalence between nil, right nilpotent evolution algebras and evolution algebras, which are defined by upper triangular matrix AA. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix AA we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.

Keywords

Cite

@article{arxiv.1004.1050,
  title  = {On evolution algebras},
  author = {J. M. Casas and M. Ladra and B. A. Omirov and U. A. Rozikov},
  journal= {arXiv preprint arXiv:1004.1050},
  year   = {2010}
}

Comments

17 pages

R2 v1 2026-06-21T15:07:28.431Z