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

The factorization problem for Jordan algebras. Applications