On the Finite Presentation of Operads

Q3 Mathematics

WSEAS Transactions on Systems and Control Pub Date : 2023-06-19 DOI:10.37394/23202.2023.22.63

Ettaki Ayoub, Elomary Mohamed Abdou, Mamouni My Ismail

引用次数: 0

Abstract

Operads were introduced to describe compositional structures arising in algebraic topology. Recently, some researches were interested in using operads in applied mathematics, to model composition of structures in logic, databases, and dynamical systems. In, we focus on finite presentation of an operad and its associated algebra. More precisely, we prove the general result stating that if an operad O has a finite presentation, then the associate O-algebra has also a corresponding one. Some application in physics, especially in wiring diagrams will be discussed.

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关于操作数的有限表示

引入运算符来描述代数拓扑中出现的组合结构。近年来，一些研究对应用数学中使用操作数来模拟逻辑、数据库和动力系统中结构的组成感兴趣。在本章中，我们重点讨论了操作符及其相关代数的有限表示。更确切地说，我们证明了一个一般结果，即如果一个操作数O有有限表示，那么它的关联O代数也有相应的有限表示。在物理学中的一些应用，特别是在接线图将讨论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

WSEAS Transactions on Systems and Control Mathematics-Control and Optimization

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Systems and Control publishes original research papers relating to systems theory and automatic control. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with systems theory, dynamical systems, linear and non-linear control, intelligent control, robotics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.