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Solid lines in axial algebras of jordan type 1/2 and Jordan algebras

Jari Desmet (UGent)
(2025) PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 153(4). p.1461-1479
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Abstract
We show that a primitive axial algebra of Jordan type 21 is a Jordan algebra if and only if every 2-generated subalgebra is solid, a notion introduced recently by Ilya Gorshkov, Sergey Shpectorov and Alexei Staroletov. As a byproduct, we show that a subalgebra generated by axes a, b is solid if and only if the associator [La,Lb] is a derivation. Moreover, we show that 2-generated subalgebras that are not solid contain precisely 3 axes.
Keywords
Axial algebras, Jordan algebras, solid subalgebras, non-associative algebras

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Citation

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MLA
Desmet, Jari. “Solid Lines in Axial Algebras of Jordan Type 1/2 and Jordan Algebras.” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 153, no. 4, 2025, pp. 1461–79, doi:10.1090/proc/17111.
APA
Desmet, J. (2025). Solid lines in axial algebras of jordan type 1/2 and Jordan algebras. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 153(4), 1461–1479. https://doi.org/10.1090/proc/17111
Chicago author-date
Desmet, Jari. 2025. “Solid Lines in Axial Algebras of Jordan Type 1/2 and Jordan Algebras.” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 153 (4): 1461–79. https://doi.org/10.1090/proc/17111.
Chicago author-date (all authors)
Desmet, Jari. 2025. “Solid Lines in Axial Algebras of Jordan Type 1/2 and Jordan Algebras.” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 153 (4): 1461–1479. doi:10.1090/proc/17111.
Vancouver
1.
Desmet J. Solid lines in axial algebras of jordan type 1/2 and Jordan algebras. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 2025;153(4):1461–79.
IEEE
[1]
J. Desmet, “Solid lines in axial algebras of jordan type 1/2 and Jordan algebras,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 153, no. 4, pp. 1461–1479, 2025.
@article{01JP21RAQ3D1PH4EC4DVF9AJEV,
  abstract     = {{We show that a primitive axial algebra of Jordan type 21 is a Jordan algebra if and only if every 2-generated subalgebra is solid, a notion introduced recently by Ilya Gorshkov, Sergey Shpectorov and Alexei Staroletov. As a byproduct, we show that a subalgebra generated by axes a, b is solid if and only if the associator [La,Lb] is a derivation. Moreover, we show that 2-generated subalgebras that are not solid contain precisely 3 axes.}},
  author       = {{Desmet, Jari}},
  issn         = {{0002-9939}},
  journal      = {{PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY}},
  keywords     = {{Axial algebras,Jordan algebras,solid subalgebras,non-associative algebras}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1461--1479}},
  title        = {{Solid lines in axial algebras of jordan type 1/2 and Jordan algebras}},
  url          = {{http://doi.org/10.1090/proc/17111}},
  volume       = {{153}},
  year         = {{2025}},
}
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