Duplicate, Bernstein algebras and evolution algebras

  • A. Conseibo Norbert Zongo University
  • S. Savadogo Norbert Zongo University
  • M. Ouattara University Pr Joseph KI-ZERBO

Abstract

In this paper, we firstly study a commutative algebra E over a field F of Char(F) ̸= 2 that satisfying dim(E2) = 1. We show that, such an algebra is an evolution algebra. Afterwards, we pay attention to commutative duplicate of a commutative algebra E. We find necessary and sufficient condition in which the duplicate D(E) is an evolution algebra. And, we finish by studying an evolution algebra that is a Bernstein algebra. We classify that algebras, up to isomorphism, in dimension ≤ 4.



{\bf Keywords}: Evolution algebras, Bernstein algebras, Duplicate, natural base.

Author Biographies

A. Conseibo, Norbert Zongo University

Universit\'e Norbert Zongo,

BP 376 Koudougou
Burkina Faso

S. Savadogo, Norbert Zongo University

Universit\'e Norbert Zongo,

BP 376 Koudougou
Burkina Faso

Published
2021-06-20
Section
Articoli