Extension, deformation and categorification of $\text{AssDer}$ pairs

Abstract

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.

Revised version

References in corpus (5)

• Deformation quantization of Poisson manifolds, I
• Higher derived brackets and homotopy algebras
• Higher-Dimensional Algebra V: 2-Groups
• Leibniz 2-algebras and twisted Courant algebroids
• 3-Lie-Rinehart Algebras

Cited by in corpus (1)

• Cohomologies of 3-Lie algebras with derivations