3 problems

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Classification conjecture for finite-dimensional composition $\mathcal{Z}_2$ -algebras
The conjecture. Every finite-dimensional composition $\mathcal{Z}_2$ -algebra is isometrically isomorphic to one of the following ten $\mathcal{Z}_2$ -algebras:
Conjectureopenclassification composition-algebras nonassociative-algebrasarXiv posted 2 days ago
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The split-octonion extension of Theorem 5.1
Let $O$ be a split-octonion algebra, and let $f:O\rightarrow O$ be an additive map. Write $O^\times$ for the set of invertible elements of $O$ . Split-octonion extension conjecture.…
Problemopencomposition-algebras functional-equations octonionsarXiv posted 2 days ago
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The generalized composition algebra isomorphism conjecture for symmetrizable Cartan matrices
Isomorphism conjecture. The homomorphism $\pi_H$ is always an isomorphism.
Conjectureopenaffine-kac-moody-algebras composition-algebras representation-theoryarXiv posted 2 days ago

Classification conjecture for finite-dimensional composition Z2\mathcal{Z}_2Z2​-algebras