Geodesic
Searching for groups related to pseudo-composition algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 526-539 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the class of idempotent-generated pseudo-composition algebras, which is a subclass of the family of axial algebras. More specifically, we utilise the group-algebra correspondence, natural to the axial framework in order to study some automorphism subgroups of such pseudo-composition algebras.
Keywords: axial algebra, Miyamoto involution
Mots-clés : pseudo-composition algebra, automorphism group. 
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V. A. Afanasev. Searching for groups related to pseudo-composition algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 526-539. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a0/

[1] GAP – Groups, Algorithms, and Programming, Version 4.12.1, , 2022 https://www.gap-system.org

[2] I. Gorshkov, A. Mamontov, A. Staroletov, Axial view on pseudo-composition algebras and train algebras of rank 3, 2023, arXiv: 2309.05237 | MR

[3] J.I. Hall, F. Rehren, S. Shpectorov, “Universal axial algebras and a theorem of Sakuma”, J. Algebra, 421 (2015), 394–424 | DOI | MR | Zbl

[4] S.M.S. Khasraw, J. McInroy, S. Shpectorov, “On the structure of axial algebras”, Trans. Am. Math. Soc., 373:3 (2020), 2135–2156 | DOI | MR | Zbl

[5] K. Meyberg, J.M. Osborn, “Pseudo-composition algebras”, Math. Z., 214:1 (1993), 67–77 | DOI | MR | Zbl

[6] J. McInroy, S.Shpectorov, Axial algebras of Jordan and Monster type, 2022, arXiv: 2209.08043 | MR