On the number of possible resonant algebras

We investigate the number of distinct resonant algebras depending on the generator content, which consists of the Lorentz generator, translation, and new additional Lorentz-like and translation-like generators. Such algebra enlargements originate directly from the Maxwell algebra and implementation...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 53; no. 35; pp. 355202 - 355212
Main Authors Durka, Remigiusz, Grela, Kamil
Format Journal Article
LanguageEnglish
Published IOP Publishing 04.09.2020
Subjects
expansion
Maxwell algebra
resonant algebras
semigroup
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ISSN1751-8113
1751-8121
DOI10.1088/1751-8121/ab9e8e

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Summary:We investigate the number of distinct resonant algebras depending on the generator content, which consists of the Lorentz generator, translation, and new additional Lorentz-like and translation-like generators. Such algebra enlargements originate directly from the Maxwell algebra and implementation of the S-expansion framework. Resonant algebras, being sub-class of the S-expanded algebras, should find use in the construction of gravity and supergravity models along some other applications. The undertaken task of establishing all the possible resonant algebras is closely related to the subject of finding commutative monoids (semigroups with the identity element) of a particular order, were we additionally enforce the parity condition.
Bibliography:JPhysA-113402.R1
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab9e8e