On the semifree resolutions of DG algebras over the enveloping DG algebras

Nasseh Saeed, Maiko Ono, Yuji Yoshino

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The goal of this paper is to construct a semifree resolution for a non-negatively graded strongly commutative DG algebra B over the enveloping DG algebra (Formula presented.), where (Formula presented.) is a DG subalgebra and B is semifree over A. Our construction of such a semifree resolution, that we denote by (Formula presented.), uses the notions of reduced bar resolution and tensor algebra of the shift of the diagonal ideal. As an application of (Formula presented.), we provide a new characterization of naïve liftability of semifree DG B-modules.

Original languageEnglish
Pages (from-to)657-667
Number of pages11
JournalCommunications in Algebra
Volume52
Issue number2
DOIs
StatePublished - 2024

Scopus Subject Areas

  • Algebra and Number Theory

Keywords

  • Bar resolution
  • DG algebra
  • DG module
  • diagonal ideal
  • enveloping DG algebra
  • lifting
  • reduced bar resolution
  • semifree resolution
  • tensor algebra
  • universal derivation

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