Obstruction to naive liftability of DG modules

2021/09/01 by Saeed Nasseh, Nasseh, Saeed, Maiko Ono +3
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2109.00607

Abstract

The notion of naive liftability of DG modules is introduced in [9] and [10]. In this paper, we study the obstruction to naive liftability along extensions A→ B of DG algebras, where B is projective as an underlying graded A-module. We show that the obstruction to naive liftability of a semifree DG B-module N is a certain cohomology class in Ext¹_B(N,N⊗_B J), where J is the diagonal ideal. Our results on obstruction class enable us to give concrete examples of DG modules that do and do not satisfy the naive lifting property.

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