## 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 language | English |
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Article number | 104854 |

Journal | Journal of Geometry and Physics |

Volume | 190 |

DOIs | |

Publication status | Published - 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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