On 3-generated axial algebras of Jordan type 1/2 Full article
| Journal |
Communications in Mathematics
ISSN: 1804-1388 , E-ISSN: 2336-1298 |
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| Output data | Year: 2025, Volume: 33, Number: 3, Article number : 4, Pages count : 12 DOI: 10.46298/cm.13307 | ||||||
| Tags | Axial algebras, Jordan type algebras | ||||||
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| Affiliations |
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Funding (1)
| 1 | Фонд развития теоретической физики и математики «БАЗИС» |
Abstract:
Axial algebras of Jordan type η are a special type of commutative nonassociative algebras. They are generated by idempotents whose adjoint operators have the minimal polynomial dividing (x − 1)x(x − η), where η is a fixed value that is not equal to 0 or 1. These algebras have restrictive multiplication rules that generalize the Peirce decomposition for idempotents in Jordan algebras. A universal 3-generated algebra of Jordan type 1 2 as an algebra with 4 parameters was constructed by I. Gorshkov and A. Staroletov. Depending on the value of the parameter, the universal algebra may contain a non-trivial form radical. In this paper, we describe all semisimple 3-generated algebras of Jordan type 1 2 over a quadratically closed field.
Cite:
Bildanov R.
, Gorshkov I.
On 3-generated axial algebras of Jordan type 1/2
Communications in Mathematics. 2025. V.33. N3. 4 :1-12. DOI: 10.46298/cm.13307 Scopus РИНЦ OpenAlex
On 3-generated axial algebras of Jordan type 1/2
Communications in Mathematics. 2025. V.33. N3. 4 :1-12. DOI: 10.46298/cm.13307 Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Mar 28, 2024 |
| Accepted: | Jun 7, 2024 |
| Published print: | Nov 1, 2024 |
| Published online: | Nov 1, 2024 |
Identifiers:
| Scopus: | 2-s2.0-85203432398 |
| Elibrary: | 74616670 |
| OpenAlex: | W4403199041 |
Citing:
| DB | Citing |
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| Scopus | 1 |