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On 3-generated axial algebras of Jordan type 1/2. / Bildanov, Ravil; Gorshkov, Ilya.

In: Communications in Mathematics, Vol. 33, No. 3, 07.10.2024.

Research output: Contribution to journal › Article › peer-review

Harvard

Bildanov, R & Gorshkov, I 2024, 'On 3-generated axial algebras of Jordan type 1/2', Communications in Mathematics, vol. 33, no. 3. https://doi.org/10.46298/cm.13307

APA

Bildanov, R., & Gorshkov, I. (2024). On 3-generated axial algebras of Jordan type 1/2. Communications in Mathematics, 33(3). https://doi.org/10.46298/cm.13307

Vancouver

Bildanov R, Gorshkov I. On 3-generated axial algebras of Jordan type 1/2. Communications in Mathematics. 2024 Oct 7;33(3). doi: 10.46298/cm.13307

Author

Bildanov, Ravil ; Gorshkov, Ilya. / On 3-generated axial algebras of Jordan type 1/2. In: Communications in Mathematics. 2024 ; Vol. 33, No. 3.

BibTeX

@article{04c260b7b4b745f28b2b57e0cbf18430,
title = "On 3-generated axial algebras of Jordan type 1/2",
abstract = "Axial algebras of Jordan type η are a special type of commutative non-associative 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.",
keywords = "Axial algebras, Jordan type algebras",
author = "Ravil Bildanov and Ilya Gorshkov",
year = "2024",
month = oct,
day = "7",
doi = "10.46298/cm.13307",
language = "English",
volume = "33",
journal = "Communications in Mathematics",
issn = "2336-1298",
publisher = "Episciences",
number = "3",

}

RIS

TY - JOUR

T1 - On 3-generated axial algebras of Jordan type 1/2

AU - Bildanov, Ravil

AU - Gorshkov, Ilya

PY - 2024/10/7

Y1 - 2024/10/7

N2 - Axial algebras of Jordan type η are a special type of commutative non-associative 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.

AB - Axial algebras of Jordan type η are a special type of commutative non-associative 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.

KW - Axial algebras

KW - Jordan type algebras

UR - https://www.mendeley.com/catalogue/9a453f91-9e71-3f17-bff1-7d559f0ebc18/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85203432398&origin=inward&txGid=1d3951756db2ddba6a6d65ee1820ad30

U2 - 10.46298/cm.13307

DO - 10.46298/cm.13307

M3 - Article

VL - 33

JO - Communications in Mathematics

JF - Communications in Mathematics

SN - 2336-1298

IS - 3

ER -

ID: 62768860