DG algebras with exterior homology

TL;DR

This paper classifies differential graded algebras with exterior algebra homology over various rings, revealing interesting examples and extending understanding of their structure and modules.

Contribution

It provides a complete classification of DGAs with exterior algebra homology over integers and prime fields for certain degrees, expanding the theoretical framework.

Findings

Complete classification over integers and prime fields

Identification of unexpectedly interesting examples

Extension of DGA and module theory

Abstract

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is the integers, or the prime field of characteristic p>0, and n is greater than or equal to -1. The examples are unexpectedly interesting.