Annales de l’institut Fourier· 2026Q1
Quillen (co)homology of divided power algebras over an operad
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- Q1SCImago
- 2026year
Short summary
This paper introduces a framework for studying the Quillen cohomology of divided power algebras over a general operad 𝒫, extending existing theories for commutative rings and Lie algebras.
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Key points
- Introduces a general framework for Quillen cohomology of divided power algebras over an operad 𝒫.
- Identifies Beck modules, derivations, and Kähler differentials in this generalized setting.
- Compares the cohomology of divided power algebras over 𝒫 with that of 𝒫-algebras.
- Works out specific examples to illustrate the theory.
AI-generated from the title and abstract; the full text is not read.
Abstract
Barr–Beck cohomology, put into the framework of model categories by Quillen, provides a cohomology theory for any algebraic structure, for example André–Quillen cohomology of commutative rings. Quillen cohomology has been studied notably for divided power algebras and restricted Lie algebras, both of which are instances of divided power algebras over an operad 𝒫 : the commutative and Lie operad respectively. In this paper, we investigate the Quillen cohomology of divided power algebras over an operad 𝒫 , identifying Beck modules, derivations, and Kähler differentials in that setup. We also compare the cohomology of divided power algebras over 𝒫 with that of 𝒫 -algebras, and work out some examples.
The authors' abstract, as published at the source. Annales de l’institut Fourier, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics