A diamond lemma for Hecke-type algebras

Elias, Ben

doi:10.1090/tran/8554

A diamond lemma for Hecke-type algebras
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Trans. Amer. Math. Soc. 375 (2022), 1883-1915 Request permission

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.

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