Filippov's identity-basis conjecture for the simple 7-dimensional Malcev algebra
Filippov's identity-basis conjecture for the simple 7-dimensional Malcev algebra
Let the simple -dimensional Malcev algebra be the algebra under consideration, and let the Filippov -polynomial be the degree- polynomial identity associated with it. Filippov's conjecture. Every polynomial identity satisfied by the simple -dimensional Malcev algebra is a consequence of the defining identities for Malcev algebras and the Filippov -polynomial of degree . This is a classical conjecture about whether the defining Malcev identities together with the degree- Filippov identity generate all polynomial identities of the simple -dimensional Malcev algebra; the supplied text does not indicate whether it has been resolved.
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Primary source
Murray R. Bremner and Andrew Douglas, “The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra”, arXiv:1108.4202 (2011).
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