A diamond lemma for Hecke-type algebras

2019/07/24 by Ben Elias, Elias, Ben · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1907.10571

Expanded addenda, minor changes to improve exposition

openalex publication_date 2019/07/24 · arxiv created 2021/08/26 · arxiv updated 2021/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Category Theory Using String Diagrams

Cited by

• Quantum wreath products and Schur--Weyl duality II

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