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arXiv · 1812.05481

Higher polynomial identities for mutations of associative algebras

Murray R. Bremner·Jose Brox·Juana Sánchez-Ortega
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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 number of new identities.

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Murray R. Bremner, Jose Brox, Juana Sánchez-Ortega. 2018-12-13. Higher polynomial identities for mutations of associative algebras. https://doi.org/10.1007/s00025-023-01986-4

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