A flow of quantum genetic Lotka-Volterra algebras on M2(C)

Farrukh Mukhamedov, Sondos M. Syam, Izzat Qaralleh

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In the present paper, we define a quantum analog of Lotka-Volterra algebras using a coalgebra scheme. This new framework provides a fresh perspective for the treatment of generic algebras. Additionally, a flow of quantum analogs of Lotka-Volterra genetic algebras is investigated. It's worth mentioning that such types of algebras are first introduced in this work. We observe that a flow of algebras is a particular type of continuous-time dynamical system, with states that are algebras and a structural constant matrix that depends on time and satisfies certain analogs of the Kolmogorov-Chapman equations. Using quantum quadratic operators, it is constructed a flow of quantum Lotka-Volterra algebras for the given multiplication. Furthermore, time-dependent behavior properties of these flow algebras are examined. The algebraic properties of the introduced flows are also studied, such as finding idempotents and examining an algebra generated by a pair of idempotents. It is shown that the later one is associative, while the flow is not associative. Additionally, derivations of the flow of the algebras are described.

Original languageEnglish
Article number104854
JournalJournal of Geometry and Physics
Volume190
DOIs
Publication statusPublished - Aug 2023

Keywords

  • Derivation
  • Flow
  • Lotka-Volterra algebra
  • Quantum quadratic operator

ASJC Scopus subject areas

  • Mathematical Physics
  • General Physics and Astronomy
  • Geometry and Topology

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