Star-closure of left coideal subalgebras of finite-dimensional C*-Hopf algebras

Determine whether every left coideal subalgebra of a finite-dimensional $C^*$-Hopf algebra is $*$-closed.

Background

The paper applies its exchange-bound method to left coideal subalgebras of finite-dimensional semisimple Hopf algebras, obtaining effective finiteness bounds. In discussing complementary formal-angle methods, it identifies additional Hopf-algebraic questions that are not resolved by the local rigidity argument.

One such question concerns whether the operator-algebraic involution is automatically preserved by every left coideal subalgebra in the finite-dimensional C∗C^*-Hopf setting. Establishing this would clarify the relationship between algebraic left coideal subalgebras and C∗C^*-compatible substructures.

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”