Filippov's identity-basis conjecture for the simple 7-dimensional Malcev algebra

Let the simple 77-dimensional Malcev algebra be the algebra under consideration, and let the Filippov hh-polynomial be the degree-55 polynomial identity associated with it. Filippov's conjecture. Every polynomial identity satisfied by the simple 77-dimensional Malcev algebra is a consequence of the defining identities for Malcev algebras and the Filippov hh-polynomial of degree 55. This is a classical conjecture about whether the defining Malcev identities together with the degree-55 Filippov identity generate all polynomial identities of the simple 77-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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