A diamond lemma for Hecke-type algebras

TL;DR

This paper extends Bergman's diamond lemma to monoidal categories with generators and relations, enabling new algebraic and categorical insights into Hecke-type algebras and their generalizations.

Contribution

It introduces a generalized diamond lemma applicable to monoidal categories and extends Manin-Schechtmann theory to non-reduced expressions.

Findings

Applicable to Coxeter groups and quiver Hecke algebras

Provides new tools for algebraic and categorical analysis

Extends existing theories to broader algebraic structures

Abstract

In this paper we give a version of Bergman's diamond lemma which applies to certain monoidal categories presented by generators and relations. In particular, it applies to: the Coxeter presentation of the symmetric groups, the quiver Hecke algebras of Khovanov-Lauda-Rouquier, the Webster tensor product algebras, and various generalizations of these. We also give an extension of Manin-Schechtmann theory to non-reduced expressions.