Abstract
We study the polynomial identities of alternative and Jordan algebras which imply the nilpotency of the algebras. In the case of a field of characteristic 0 we describe all these systems of identities as well as all almost nilpotent varieties of alternative and Jordan algebras. In particular, we establish a connection between the Engel identity for the Lie algebras and the standard identity for the Jordan algebras.
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Popov, A.V. Nilpotency of Alternative and Jordan Algebras. Sib Math J 62, 148–158 (2021). https://doi.org/10.1134/S003744662101016X
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DOI: https://doi.org/10.1134/S003744662101016X
Keywords
- Jordan algebras
- alternative algebras
- almost nilpotent varieties
- Nagata–Higman Theorem
- Engel identity
- standard Jordan identity