Winter 2024 OBSTRUCTION TO NAÏVE LIFTABILITY OF DG MODULES
Saeed Nasseh, Maiko Ono, Yuji Yoshino
J. Commut. Algebra 16(4): 459-475 (Winter 2024). DOI: 10.1216/jca.2024.16.459

Abstract

In previous work we introduced the notion of naïve liftability of DG modules. The main purpose of this paper is to explicitly describe the obstruction to naïve liftability along extensions AB of DG algebras, where B is projective as an underlying graded A-module. In particular, we give an explicit description of a DG B-module homomorphism which defines the obstruction to naïve liftability of a semifree DG B-module N as a certain cohomology class in ExtB1(N,NBJ), where J is the diagonal ideal. Our results on the obstruction class enable us to give concrete examples of DG modules that do and do not satisfy the naïve lifting property.

Citation

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Saeed Nasseh. Maiko Ono. Yuji Yoshino. "OBSTRUCTION TO NAÏVE LIFTABILITY OF DG MODULES." J. Commut. Algebra 16 (4) 459 - 475, Winter 2024. https://doi.org/10.1216/jca.2024.16.459

Information

Received: 31 July 2022; Revised: 13 December 2023; Accepted: 5 March 2024; Published: Winter 2024
First available in Project Euclid: 6 January 2025

Digital Object Identifier: 10.1216/jca.2024.16.459

Subjects:
Primary: 13D07 , 16E45

Keywords: DG algebra , DG module , lifting , naïve lifting , weak lifting

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

Vol.16 • No. 4 • Winter 2024
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