A diamond lemma for Hecke-type algebras

Author:

Elias Ben

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.

Funder

National Science Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference19 articles.

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3. Gröbner-Shirshov bases for Coxeter groups;Bokut, L. A.;Comm. Algebra,2001

4. An algorithmic criterion for the solvability of a system of algebraic equations [ MR0268178 (42 #3077)];Buchberger, Bruno,1998

5. Gröbner bases for operads;Dotsenko, Vladimir;Duke Math. J.,2010

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