Alternating quiver Hecke algebras

TL;DR

This paper introduces alternating quiver Hecke algebras, a new family derived from fixed-point subalgebras of quiver Hecke algebras under a sign map, with a basis theorem and generator-relations presentation.

Contribution

It defines and studies the structure of alternating quiver Hecke algebras, providing a basis theorem and a presentation similar to KLR algebras, for simply-laced quivers.

Findings

Established a basis theorem for the new algebras.

Provided a generator and relations presentation.

Showed structural similarity to KLR algebras.

Abstract

For simply-laced quivers, we consider the fixed-point subalgebra of the quiver Hecke algebra under the homogeneous sign map. This leads to a new family of algebras we call alternating quiver Hecke algebras. We give a basis theorem and a presentation by generators and relations which is strikingly similar to the KLR presentation for quiver Hecke algebras.