Ravil Bildanov ; Ilya Gorshkov - On 3-generated axial algebras of Jordan type 12

cm:13307 - Communications in Mathematics, October 7, 2024, Volume 33 (2025), Issue 3 (Special issue: European Non-Associative Algebra Seminar) - https://doi.org/10.46298/cm.13307
On 3-generated axial algebras of Jordan type 12Article

Authors: Ravil Bildanov ; Ilya Gorshkov

    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 (x1)x(xη), 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 12 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 12 over a quadratically closed field.


    Volume: Volume 33 (2025), Issue 3 (Special issue: European Non-Associative Algebra Seminar)
    Published on: October 7, 2024
    Accepted on: June 7, 2024
    Submitted on: March 28, 2024
    Keywords: Mathematics - Rings and Algebras,Mathematics - Group Theory

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