The differential graded odd nilHecke algebra

TL;DR

This paper introduces differentials into the odd nilHecke algebra and its thick calculus, revealing that their differential graded Grothendieck groups correspond to quantum sl(2) at a fourth root of unity.

Contribution

It provides a new differential graded structure on the odd nilHecke algebra and links it to quantum groups at roots of unity.

Findings

Differential graded structures are established on the odd nilHecke algebra.

Grothendieck groups match positive parts of quantum sl(2) at a fourth root of unity.

New diagrammatic calculus with differentials is developed.

Abstract

We equip the odd nilHecke algebra and its associated thick calculus category with digrammatically local differentials. The resulting differential graded Grothendieck groups are isomorphic to two different forms of the positive part of quantum sl(2) at a fourth root of unity.