Morita invariants of quasitriangular coideal subalgebras

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.

v2: 17 pages. Title change. Updated Theorem 1.5(a)/4.8. Added and incorporated Lemma 2.12. Updated Proposition 3.5(b). To appear in JPAA