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arXiv · 2408.07078

Shift associative algebras

Hani Abdelwahab·Ivan Kaygorodov·Bauyrzhan Sartayev
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Abstract

We present a comprehensive study of algebras satisfying the identity $(xy)z=y(zx),$ named as shift associative algebras. Our research shows that these algebras are related to many interesting identities. In particular, they are related to anti-Poisson-Jordan algebras and algebras of associative type $\sigma$. We study algebras of associative type $\sigma$ to be Koszul and self-dual. A basis of the free shift associative algebra generated by a countable set $X$ was constructed. An analog of Wedderburn-Artin's theorem was established. The algebraic and geometric classifications of complex $4$-dimensional shift associative algebras are given. In particular, we proved that the first non-associative shift associative algebra appears only in dimension $5$.

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Hani Abdelwahab, Ivan Kaygorodov, Bauyrzhan Sartayev. 2024-08-04. Shift associative algebras. https://arxiv.org/abs/2408.07078

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