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arXiv · 2402.06924

Extended derivations of algebras

Edison Alberto Fernández-Culma
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Abstract

We study the concept of extended derivations of algebras which expands diverse definitions of generalized derivations given in the literature. We concentrate on the family of the anti-commutative algebras and classify such spaces of derivations by considering a suitable notion of equivalence when we restrict attention to such algebras. Afterwards, we investigate a link between the well-known $(\alpha,\beta,\gamma)$-derivations and some new extended derivations obtained in the above-mentioned classification. Finally, we present applications of extended derivations to study degenerations of algebras.

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Edison Alberto Fernández-Culma. 2024-02-10. Extended derivations of algebras. https://arxiv.org/abs/2402.06924

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