Divided powers and K\"ahler differentials

TL;DR

This paper explores the structure of divided power algebras, identifying their universal enveloping algebra and K"ahler differentials over general rings, thereby simplifying and extending previous research.

Contribution

It provides a unified framework for understanding the universal enveloping algebra and K"ahler differentials of divided power algebras over arbitrary commutative rings, generalizing prior results.

Findings

Identification of universal enveloping algebra for divided power algebras

Explicit description of K"ahler differentials in this context

Simplification and generalization of Roby and Dokas's work

Abstract

Divided power algebras form an important variety of non-binary universal algebras. We identify the universal enveloping algebra and K\"ahler differentials associated to a divided power algebra over a general commutative ring, simplifying and generalizing work of Roby and Dokas.