In this paper, we consider associative algebras equipped with derivations. A pair consisting of an associative algebra and a distinguished derivation is called an AssDer pair. We study central extensions and formal one-parameter deformations of AssDer pairs in terms of cohomology. Finally, we define 2-derivations on associative 2-algebras and show that the category of associative 2-algebras with 2-derivations is equivalent to the category of 2-term A_\infty-algebras with homotopy derivations.
Keywords: AssDer pair, Hochschild cohomology, central extension, deformation, homotopy derivation, categorification.
2020 MSC: 16E40, 16S80, 16W25, 18N25, 18N40.
Theory and Applications of Categories, Vol. 45, 2026, No. 1, pp 1-32.
Published 2026-01-05.
TAC Home