The nil-Brauer category

Abstract

We introduce the nil-Brauer category and prove a basis theorem for its morphism spaces. This basis theorem is an essential ingredient required to prove that nil-Brauer categorifies the split iquantum group of rank one. As this iquantum group is a basic building block for $ı$-quantum groups of higher rank, we expect that the nil-Brauer category will play a role in future developments related to the categorification of quantum symmetric pairs.

v3: this revision corrects a sign error in the formula (4.2) in the published text