The beginnings of the theory of Hopf algebras

TL;DR

This paper explores the historical origins of Hopf algebras, highlighting their development from algebraic topology and algebraic group theory in the mid-20th century.

Contribution

It provides a historical overview of the early development and foundational papers that led to the formation of Hopf algebra theory.

Findings

Identifies key historical sources from the 1940s-60s

Highlights the influence of algebraic topology and group theory

Transcribes original foundational papers

Abstract

We consider issues related to the origins, sources and initial motivations of the theory of Hopf algebras. We consider the two main sources of primeval development: algebraic topology and algebraic group theory. Hopf algebras are named from the work of Heinz Hopf in the 1940's. In this note we trace the infancy of the subject back to papers from the 40's, 50's and 60's in the two areas mentioned above. Many times we just describe -- and/or transcribe parts of -- some of the relevant original papers on the subject.