Shift associative algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913467719483392 |
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| author | Abdelwahab, Hani Kaygorodov, Ivan Sartayev, Bauyrzhan |
| author_facet | Abdelwahab, Hani Kaygorodov, Ivan Sartayev, Bauyrzhan |
| contents | 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 $5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shift associative algebras Abdelwahab, Hani Kaygorodov, Ivan Sartayev, Bauyrzhan Rings and Algebras 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 $5$. |
| title | Shift associative algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2408.07078 |