3 problems

Globality conjecture. Every dual pair $(M,\mathcal{L})$ of Malcev algebras and their corresponding Moufang loops is global.

Minimal dimension conjecture. Every Malcev algebra of the second type of dimension $<23$ over a field of characteristic $0$ is an algebra of the first type.

Let the simple $7$-dimensional Malcev algebra be the algebra under consideration, and let the Filippov $h$-polynomial be the degree-$5$ polynomial identity associated with it. Fili…