Higher Polynomial Identities for Mutations of Associative Algebras

We study polynomial identities satisfied by the mutation product [Formula: see text] on the underlying vector space of an associative algebra A, where p, q are fixed elements of A. We simplify known results for identities in degree 4, proving that only two identities are necessary and sufficient to...

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Autores principales: Bremner, Murray R., Brox, Jose, Sánchez-Ortega, Juana
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10517047/
https://www.ncbi.nlm.nih.gov/pubmed/37744678
http://dx.doi.org/10.1007/s00025-023-01986-4
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author Bremner, Murray R.
Brox, Jose
Sánchez-Ortega, Juana
author_facet Bremner, Murray R.
Brox, Jose
Sánchez-Ortega, Juana
author_sort Bremner, Murray R.
collection PubMed
description We study polynomial identities satisfied by the mutation product [Formula: see text] on the underlying vector space of an associative algebra A, where p, q are fixed elements of A. We simplify known results for identities in degree 4, proving that only two identities are necessary and sufficient to generate them all; in degree 5, we show that adding one new identity suffices; in degree 6, we demonstrate the existence of a significant number of new identities, which induce us to conjecture that the variety generated by mutation algebras of associative algebras is not finitely based.
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spelling pubmed-105170472023-09-24 Higher Polynomial Identities for Mutations of Associative Algebras Bremner, Murray R. Brox, Jose Sánchez-Ortega, Juana Results Math Article We study polynomial identities satisfied by the mutation product [Formula: see text] on the underlying vector space of an associative algebra A, where p, q are fixed elements of A. We simplify known results for identities in degree 4, proving that only two identities are necessary and sufficient to generate them all; in degree 5, we show that adding one new identity suffices; in degree 6, we demonstrate the existence of a significant number of new identities, which induce us to conjecture that the variety generated by mutation algebras of associative algebras is not finitely based. Springer International Publishing 2023-09-22 2023 /pmc/articles/PMC10517047/ /pubmed/37744678 http://dx.doi.org/10.1007/s00025-023-01986-4 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Bremner, Murray R.
Brox, Jose
Sánchez-Ortega, Juana
Higher Polynomial Identities for Mutations of Associative Algebras
title Higher Polynomial Identities for Mutations of Associative Algebras
title_full Higher Polynomial Identities for Mutations of Associative Algebras
title_fullStr Higher Polynomial Identities for Mutations of Associative Algebras
title_full_unstemmed Higher Polynomial Identities for Mutations of Associative Algebras
title_short Higher Polynomial Identities for Mutations of Associative Algebras
title_sort higher polynomial identities for mutations of associative algebras
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10517047/
https://www.ncbi.nlm.nih.gov/pubmed/37744678
http://dx.doi.org/10.1007/s00025-023-01986-4
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