---
tag: 4F4Z3Q5ZFY
kind: concept
name: Rota–Baxter algebra
aliases: [baxter-operator, rota-baxter]
sources:
  - wikipedia: en:21091721@r1372853264
    locator: Rota–Baxter algebra
    note: adopted
    mention: wikipedia://en/21091721
    sections: [Summary]
same_as:
  wikidata: Q7370348
  wikipedia: Rota–Baxter algebra
inventory: [C6MJPD0HX1]
---

## Summary

In mathematics, a **Rota–Baxter algebra** is an associative algebra, together with a particular [[linear map|0NRYHJPQG2]] $R$ which satisfies the **Rota–Baxter identity**. It appeared first in the work of the American mathematician Glen E. Baxter in the realm of [[probability theory|0RWE7CPJ32]]. Baxter's work was further explored from different angles by Gian-Carlo Rota, Pierre Cartier, and Frederic V. Atkinson, among others. Baxter’s derivation of this identity that later bore his name emanated from some of the fundamental results of the famous probabilist Frank Spitzer in [[random walk|04VZE3FZXF]] theory.