Coherence of the lattice of left coideal subalgebras

Determine whether the lattice of left coideal subalgebras of a finite-dimensional $C^*$-Hopf algebra is coherent.

Background

The paper notes that the formal-angle framework yields coherent pairs and coherent sublattices and identifies lattice-theoretic questions for Hopf-algebraic substructures. Its local Ocneanu-rigidity results establish finiteness and quantitative bounds but do not settle whether the entire lattice of left coideal subalgebras satisfies the stronger coherence property.

The unresolved issue is specifically whether coherence is forced for the lattice associated with a finite-dimensional C∗C^*-Hopf algebra.

References

It also isolates natural Hopf-algebraic questions, including whether left coideal subalgebras of finite-dimensional $C*$-Hopf algebras must be $*$-closed and whether their lattice is coherent.

— Local Ocneanu rigidity for separable algebra objects  (2609.10440 - Azzouz et al., 9 Sep 2026) in Section “Scope, sharpness, and open directions,” subsection “Local Ocneanu rigidity and the formal-angle method”