9 problems

Let the relevant traces be the partial traces of monodromy matrices acting on the tensor product of the spin-chain Hilbert space and the functional space of differential functions…

Dual-basis conjecture. The elements $i_{(1)}\oB i_{(2)}$ form a dual basis for the Frobenius homomorphism $\Fi_B$. This conjecture is suggested by the corresponding double-algebra…

Let $R$ and $S$ be rings, let $L$ be a $\times_R$-bialgebra, and let $P$ and $Q$ implement the Morita equivalence between $R$ and $S$. Write…

Equivalence conjecture. This construction is equivalent to the construction due to A. Ocneanu.

Let $G$ be a reductive group, let ${}^L\!G$ be its Langlands dual group, and let $\Sigma$ be a smooth curve. Write $\textnormal{Bun}_G(\Sigma)$ and…

Let a universal quantization of Lie bialgebroids mean a quantization whose formulas are given by expansions in terms of graphs with universal coefficients, and let a quantum groupo…

Let $(E,E^*)$ be a Lie bialgebroid. A quantization is a topological deformation of the standard associative bialgebroid structure on the universal enveloping algebra…

A $C^*$-quantum groupoid is an algebraic generalization of a $C^*$-Hopf algebra, and the construction in the cited work extends Kitaev models from Hopf-algebra inputs to this setti…

A locally compact groupoid or quantum groupoid is considered together with convolution products of functions having locally compact support. Conjecture. Similar results to the corr…