Bruhat order and nil-Hecke algebras for Weyl groupoids

TL;DR

This paper introduces nil-Hecke algebras for Weyl groupoids, establishing a basis and properties that enable defining a Bruhat order in this generalized setting, extending classical algebraic structures.

Contribution

It presents the first construction of nil-Hecke algebras for Weyl groupoids and develops a Bruhat order framework for these structures.

Findings

Defined a basis for nil-Hecke algebras of Weyl groupoids

Established properties of these algebras

Introduced a Bruhat order for Weyl groupoids

Abstract

We introduce nil-Hecke algebras for Weyl groupoids. We describe a basis and some properties of these algebras which lead to a notion of Bruhat order for Weyl groupoids.