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The factorization problem for Jordan algebras: applications

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Abstract

We investigate the factorization problem as well as the classifying complements problem in the setting of Jordan algebras. Matched pairs of Jordan algebras and the corresponding bicrossed products are introduced. It is shown that any Jordan algebra which factorizes through two given Jordan algebras is isomorphic to a bicrossed product associated to a certain matched pair between the same two Jordan algebras. Furthermore, a new type of deformation of a Jordan algebra is proposed as the main step towards solving the classifying complements problem.

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Acknowledgements

This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI–UEFISCDI, project number PN-III-P4-ID-PCE-2020-0458, within PNCDI III.

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Authors and Affiliations

  1. Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    A. L. Agore & G. Militaru

  2. Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    A. L. Agore

  3. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014, Bucharest 1, Romania

    G. Militaru

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  1. A. L. Agore
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  2. G. Militaru
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Correspondence to A. L. Agore.

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Agore, A.L., Militaru, G. The factorization problem for Jordan algebras: applications. Collect. Math. 74, 687–701 (2023). https://doi.org/10.1007/s13348-022-00369-2

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