The tangle and planar quasi-partition algebra isomorphism conjecture

Let

$$be a field with$$

, let

$$, and let$$

and

$$be the tangle and planar quasi-partition algebras, respectively. **The tangle\quasi-partition isomorphism conjecture.** There \exists$$

such that

$$\mathcal{T}_n(\gamma)\cong\mathcal{P}\mathcal{Q}\mathcal{P}_n(\beta).$$

The conjecture proposes that these algebras are isomorphic for a suitable choice of parameter. The supplied text gives no proof or resolution.