一个用于执行李代数S-展开的Java库
A Java library to perform S-expansions of Lie algebras
AI总结：
本研究针对李代数收缩法的推广需求，聚焦S-展开方法，开发了可自动化执行任意半群下李代数S-展开的Java库，提供示例程序便于非Java专家修改使用，并展望了后续发展与应用方向。
摘要：
收缩法是一种可建立李代数之间非平凡关系的方法，已在数学和理论物理领域得到成功应用。本文研究收缩过程的推广形式，重点关注所谓的S-展开方法，因为该方法涵盖了大多数其他广义收缩方法。从本质上讲，S-展开将李代数$\u27e8G\u27e9$与有限阿贝尔半群$S$相结合，以定义新的S-展开代数。在介绍了本文使用的主要要素之后，我们提出了一个可实现S-展开过程自动化的Java库。借助该计算工具，我们能够表示李代数和半群，从而可以使用任意半群执行李代数的S-展开。我们阐释了库方法的构建方式与工作原理，随后给出了一组旨在解决不同问题的示例程序。这些示例的呈现方式使得任何用户都能轻松修改它们以执行自己的计算，而不必是Java专家。最后，我们对进一步的开发方向和可能的新应用进行了一些评述。
英文摘要：
The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had succesful applications in both mathematics and theoretical physics. This work deals with generalizations of the contraction procedure with a main focus in the so called S-expansion method as it includes most of the other generalized contractions. Basically, the S-exansion combines a Lie algebra $\mathcal{G}$ with a finite abelian semigroup $S$ in order to define new S-expanded algebras. After giving a description of the main ingredients used in this paper, we present a Java library that automatizes the S-expansion procedure. With this computational tool we are able to represent Lie algebras and semigroups, so we can perform S-expansions of Lie algebras using arbitrary semigroups. We explain how the library methods has been constructed and how they work; then we give a set of example programs aimed to solve different problems. They are presented so that any user can easily modify them to perform his own calculations, without being necessarily an expert in Java. Finally, some comments about further developements and possible new applications are made.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
