2024/08/04 by Hani Abdelwahab, Ivan Kaygorodov, Abdelwahab, Hani +3 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2408.07078
openalex publication_date 2024/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 σ. We study algebras of associative type σ 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.