Quillen (co)homology of divided power algebras over an operad
Abstract
BarrBeck cohomology, put into the framework of model categories by Quillen, provides a cohomology theory for any algebraic structure, for example AndréQuillen 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2024
 DOI:
 10.48550/arXiv.2403.18049
 arXiv:
 arXiv:2403.18049
 Bibcode:
 2024arXiv240318049D
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Algebraic Topology;
 Primary 18M70;
 Secondary 17B50;
 17B56;
 13D03
 EPrint:
 Minor corrections