Higher polynomial identities for mutations of associative algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866916872871477248 |
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| author | Bremner, Murray R. Brox, Jose Sánchez-Ortega, Juana |
| author_facet | Bremner, Murray R. Brox, Jose Sánchez-Ortega, Juana |
| contents | 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 number of new identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_05481 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Higher polynomial identities for mutations of associative algebras Bremner, Murray R. Brox, Jose Sánchez-Ortega, Juana Rings and Algebras Primary 18M70, Secondary 16R10, 16W10, 17A30, 17A50, 17B60, 17C65, 17D25, 68W30 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 number of new identities. |
| title | Higher polynomial identities for mutations of associative algebras |
| topic | Rings and Algebras Primary 18M70, Secondary 16R10, 16W10, 17A30, 17A50, 17B60, 17C65, 17D25, 68W30 |
| url | https://arxiv.org/abs/1812.05481 |