Lotka–Volterra coalgebras

Abstract

We study Lotka–Volterra coalgebras, a new family of nonassociative coalgebras emerging from population genetics. We focus on their defining algebraic properties and deal with characterizing the existence of counital and character maps. We also provide a classification of their basis elements into (co)algebraically persistent and transient generators resulting in a semidirect sum decomposition of Lotka–Volterra coalgebras.

Keywords:

• Lotka–Volterra coalgebra
• baric coalgebra
• semidirect sum decomposition

Acknowledgments

This paper was written while the third author was visiting the Department of Mathematics of the University of Chile, supported by FONDECYT 1170547, and wants to thank the members of the department there for their hospitality. The authors want to thank the referee for his/her comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are supported by Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) grant 1170547. The third author is also supported by MTM2017-83506-C2-1-P (AEI/FEDER, UE).