Axial view on pseudo-composition algebras and train algebras of rank 3
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914679513677824 |
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| author | Gorshkov, Ilya Mamontov, Andrey Staroletov, Alexey |
| author_facet | Gorshkov, Ilya Mamontov, Andrey Staroletov, Alexey |
| contents | We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompositions of idempotents in these classes of algebras.
The corresponding axial algebras are called $\mathcal{PC}(η)$-axial algebras, where $η$ is an element of the ground field. As a first step towards their classification, we describe $2-$ and $3$-generated subalgebras of such algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05237 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Axial view on pseudo-composition algebras and train algebras of rank 3 Gorshkov, Ilya Mamontov, Andrey Staroletov, Alexey Rings and Algebras 17A99 (Primary) 17C27, 17D92 (Secondary) We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompositions of idempotents in these classes of algebras. The corresponding axial algebras are called $\mathcal{PC}(η)$-axial algebras, where $η$ is an element of the ground field. As a first step towards their classification, we describe $2-$ and $3$-generated subalgebras of such algebras. |
| title | Axial view on pseudo-composition algebras and train algebras of rank 3 |
| topic | Rings and Algebras 17A99 (Primary) 17C27, 17D92 (Secondary) |
| url | https://arxiv.org/abs/2309.05237 |