A semisimple subcategory of Khovanov's Heisenberg category

We show the existence of a semisimple replete subcategory of Khovanov’s Heisenberg category that retains the isomorphism data of objects for the full category. This leads to a noncommutative tensor-triangular geometric example of a monoidal triangulated category whose Balmer spectrum satisfies the tensor product property but which contains one-sided thick tensor-ideals that are not two-sided, and whose standard support varieties fail to classify one-sided thick tensor-ideals.

💡 Research Summary

The paper investigates a striking phenomenon in non‑commutative tensor‑triangular geometry by focusing on Khovanov’s Heisenberg category ( \mathcal{H}eis ). The author’s main achievement is the construction of a replete semisimple subcategory ( \mathcal{H}eis^{\mathsf{s}} \subset \mathcal{H}eis ) that preserves all isomorphism data of objects while discarding the more intricate morphism structure. Concretely, every object of ( \mathcal{H}eis ) is isomorphic to a direct sum of the simple objects \