A diamond lemma for Hecke-type algebras

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.

Expanded addenda, minor changes to improve exposition

Cited by in corpus (2)

• Actions of sl_2 on algebras appearing in categorification
• On Bergman's Diamond Lemma for Ring Theory