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Divided power algebras with derivation Ikonicoff, Sacha


Classical divided power algebras are commutative associative algebras endowed with `divided power' monomial operations. They were introduced by Cartan in the 1950's in the study of the homology of Eilenberg-MacLane spaces, and appear in several branches of mathematics, such as crystalline cohomology and deformation theory. In this talk, we will investigate divided power algebras with derivation, and identify the most natural compatibility relation between a derivation and the divided power operations. The work of Keigher and Pritchard on formal divided power series (also called Hurwitz series) suggests a certain `power rule'. We will prove, using the framework of operads, that this power rule gives a reasonable definition for a divided power algebra with derivation. We will extend this result to a more general notion of divided power algebras, such as restricted Lie algebras, with derivation.

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