View in EDS

A Java Library to Perform S -Expansions of Lie Algebras.

Saved in:
Bibliographic Details
Title: A Java Library to Perform S -Expansions of Lie Algebras.
Authors: Inostroza, Carlos, Kondrashuk, Igor, Merino, Nelson, Nadal, Felip
Source: Axioms (2075-1680); Oct2025, Vol. 14 Issue 10, p735, 55p
Subject Terms: LIE algebras, SEMIGROUPS (Algebra), MATHEMATICS, MATHEMATICAL physics, SOFTWARE libraries (Computer programming), UTILITIES (Computer programs)
Abstract: The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had successful applications in both mathematics and theoretical physics. This work deals with generalizations of the contraction procedure, with a main focus on the so-called S-expansion method, as it includes most of the other generalized contractions. Basically, the S-expansion combines a Lie algebra 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 automates 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 have 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 their own calculations, without necessarily being an expert in Java. Finally, some comments about further developments and possible new applications are made. [ABSTRACT FROM AUTHOR]
Copyright of Axioms (2075-1680) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Complementary Index
Description
Abstract:The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had successful applications in both mathematics and theoretical physics. This work deals with generalizations of the contraction procedure, with a main focus on the so-called S-expansion method, as it includes most of the other generalized contractions. Basically, the S-expansion combines a Lie algebra 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 automates 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 have 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 their own calculations, without necessarily being an expert in Java. Finally, some comments about further developments and possible new applications are made. [ABSTRACT FROM AUTHOR]
ISSN:20751680
DOI:10.3390/axioms14100735