Infinite-dimensional Nichols algebras for specified Yetter–Drinfeld modules

Let $M\langle(xy,x)\rangle$, $M\langle(y,xy)\rangle$, and $W^{b_1,-1}$ denote the Yetter–Drinfeld modules introduced in the paper, and let $\mathfrak{B}(-)$ denote their Nichols algebra. The conjecture.

$$\dim\mathfrak{B}\left(M\langle(xy,x)\rangle \oplus W^{b_1,-1}\right)=\infty =\dim\mathfrak{B}\left(M\langle(y,xy)\rangle \oplus W^{b_1,-1}\right)$$

for $b_1=\pm 1$. The claim concerns the infinite-dimensionality of Nichols algebras arising in the classification of finite-dimensional Hopf algebras over the Kac–Paljutkin algebra $H_8$; the supplied text gives no evidence that it has been proved or disproved.