8 problems

Finiteness conjecture. In any given dimension, the number of non-isomorphic weak Hopf algebras $H$ with this property is finite.

Uniqueness conjecture. In $U_q^w$ and $U_q^v$, the only zero divisors annihilating all generators are $J_w-1$ and $J_v-1$, respectively.

Consider $(1+1)$D phases equipped with weak Hopf symmetry, as realized by lattice models whose symmetries are subalgebras of $H \times \hat{H}$ for a weak Hopf algebra $H$ and its…

Weak Hopf exponent conjecture. There exist positive integers $\eta$ and $\nu$ such that

Boundary duality conjecture. The duality for the boundary can also be characterized by twist deformation of the two $W$-comodule algebras $\mathfrak{A}_1$ and $\mathfrak{A}_2$.

Let the Lee-Yang C-weak Hopf algebra be the algebra described in Example, and let the associated RFP MPDOs be the renormalization fixed-point matrix product density operators const…

Let RFP MPDOs be the renormalization fixed-point matrix product density operators constructed from biconnected C-weak Hopf algebras. The general phase classification of these state…

Pivotality conjecture. Every semisimple weak Hopf algebra is pivotal.