Geodesic
Quasi-definite primitive axial algebras of Jordan type half
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 833-846.

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Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents whose action on an algebra is semisimple, and the fusion laws on the products between eigenvectors for these idempotents are fulfilled. We find the sufficient conditions in terms of the Frobenius form and the properties of idempotents under which an axial algebra of Jordan type half is unital.
Keywords: axial algebra of Jordan type, semisimplicity.
Mots-clés : Frobenius form 
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I. B. Gorshkov; V. Yu. Gubarev. Quasi-definite primitive axial algebras of Jordan type half. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 833-846. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a7/

[1] A.A. Albert, “A structure theory for Jordan algebras”, Ann. Math. (2), 48 (1947), 546–567 | DOI | MR | Zbl

[2] https://github.com/GubarevV/Quasi-definite-axial-algebras

[3] I. Gorshkov, A. Staroletov, “On primitive 3-generated axial algebras of Jordan type”, J. Algebra, 563 (2020), 74–99 | DOI | MR | Zbl

[4] J.I. Hall, F. Rehren, S. Shpectorov, “Primitive axial algebras of Jordan type”, J. Algebra, 437 (2015), 79–115 | DOI | MR | Zbl

[5] J.I. Hall, Y. Segev, S. Shpectorov, “On primitive axial algebras of Jordan type”, Bull. Inst. Math. Acad. Sin. (N.S.), 13:4 (2018), 397–409 | MR | Zbl

[6] A.A. Ivanov, The monster group and majorana involutions, Cambridge University Press, Cambridge, 2009 | MR | Zbl

[7] T. De Medts, F. Rehren, “Jordan algebras and 3-transposition groups”, J. Algebra, 478 (2017), 318–340 | DOI | MR | Zbl