Equality of local and ordinary derivations for genetic Volterra algebras
Let be an -dimensional genetic Volterra algebra. A local derivation is a linear map on such that, for every , there exists a derivation with . The derivations of form the usual class of linear maps satisfying the derivation identity.
Local-derivation conjecture. The category of local derivations of coincides with the category of derivations of .
The preceding theorem establishes this equality for three-dimensional genetic Volterra algebras. The assertion asks whether the same conclusion holds in every dimension.
References
Primary source
Rasul Ganikhodzhaev, Farrukh Mukhamedov, Abror Pirnapasov and Izzat Qaralleh, “Genetic Volterra algebras and their derivations”, arXiv:1706.01667 (2017).
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