Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/111160| Title: | Higher Polynomial Identities for Mutations of Associative Algebras | Authors: | Bremner, Murray R. Brox, Jose Sánchez-Ortega, Juana |
Keywords: | Mutation algebras; Lie-admissible; Jordan-admissible; polynomial identities; algebraic operads; computer algebra; theoretical particlephysics | Issue Date: | 2023 | Publisher: | Springer Nature | Project: | Open access funding provided by FCT—FCCN (b-on). Murray Bremner was supported by the Discovery Grant Algebraic Operads from NSERC, the Natural Sciences and Engineering Research Council of Canada. Jose Brox was supported by the Portuguese Government through grant SFRH/BPD/118665/ 2016 (FCT/Centro 2020/Portugal 2020/ESF). Juana S´anchez-Ortega was supported by a CSUR grant from the NRF, the National Research Foundation of South Africa. This work was partially supported by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2020, funded through FCT/MCTES, Funda¸c˜ao para a Ciˆencia e a Tecnologia/Minist´erio da Ciˆencia, Tecnologia e Ensino Superior de Portugal. | Serial title, monograph or event: | Results in Mathematics | Volume: | 78 | Issue: | 6 | Abstract: | We study polynomial identities satisfied by the mutation product xpy-yqx 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. | URI: | https://hdl.handle.net/10316/111160 | ISSN: | 1422-6383 1420-9012 |
DOI: | 10.1007/s00025-023-01986-4 | Rights: | openAccess |
| Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Higher-Polynomial-Identities-for-Mutations-of-Associative-AlgebrasResults-in-Mathematics.pdf | 507.64 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License
