6 problems

Let $\mathfrak{g}$ be a Lie algebra, let $U(\mathfrak{g})[[{\mathchar'26\mkern-9muh}]]$ be its formal power-series enveloping algebra with standard coproduct $\Delta_0$, let $\Phi$…

Let $H$ be a Hopf algebra, let $B$ be a left coideal subalgebra, and let $(H/B^+H)^\ast\#B$ be the associated left partially dualized quasi-Hopf algebra. In Remark on invertibility…

Let $L_2$ be the $A_1$ root lattice and let $V:=V_{L_2}$ be the corresponding lattice vertex operator algebra. Let $SU(2)$ be the universal central extension of $SO_3(\mathbb{R})$,…

Let $p\geq 2$, let $q=e^{\pi i/p}$, let $\overline{U}^{(\Phi)}_{q} s\ell(2)$ be the factorisable ribbon quasi-Hopf algebra described above, and let $\mathcal{W}(p)$ be the triplet…

Let $\mathrm N$ be the parameter specifying the number of symplectic fermion pairs, let $\beta$ be the scalar used in the ribbon structure, and let…

A quasi-bialgebra is an algebraic structure with coproduct, counit, and associator satisfying the quasi-bialgebra axioms; a preantipode is a map satisfying the three preantipode ax…