Morita invariants of quasitriangular coideal subalgebras

TL;DR

This paper develops invariants for categories of quasitriangular coideal subalgebras using braid group representations of Coxeter types BC and D, extending known methods from type A and providing concrete examples and classifications.

Contribution

It introduces a new approach to invariants of coideal subalgebra categories via braid group representations, generalizing previous type A results.

Findings

Constructed invariants for quasitriangular coideal subalgebra categories.

Provided classification results for K-matrices.

Included concrete examples of the invariants.

Abstract

We use representations of braid groups of Coxeter types BC and D to produce invariants of representation categories of quasitriangular coideal subalgebras. Such categories form a prevalent class of braided module categories. This is analogous to how representations of braid groups of Coxeter type A produce invariants of representation categories of quasitriangular Hopf algebras, a prevalent class of braided monoidal categories. This work also includes concrete examples, and classification results for $K$-matrices of quasitriangular coideal subalgebras.