Equality of local and ordinary derivations for genetic Volterra algebras
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.
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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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