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arXiv · 2002.11415

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

Apurba Das·Ashis Mandal
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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.

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BibTeXRIS

Apurba Das, Ashis Mandal. 2020-02-26. Extension, deformation and categorification of $\text{AssDer}$ pairs. https://arxiv.org/abs/2002.11415

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