---
tag: XE3HPHDC5J
kind: concept
name: Jucys–Murphy element
aliases: [jucys-murphy-elements]
sources:
  - wikipedia: en:24153642@r1214487075
    locator: Jucys–Murphy element
    note: adopted
    mention: wikipedia://en/24153642
    sections: [Summary]
same_as:
  wikidata: Q4531156
  wikipedia: Jucys–Murphy element
inventory: [GXVV77SY50]
---

## Summary

In mathematics, the **Jucys–Murphy elements** in the group algebra $\mathbb{C} [S_n]$ of the [[symmetric group|0515A6D2Y1]], named after Algimantas Adolfas Jucys and G. E. Murphy, are defined as a sum of transpositions by the formula: