6 problems

Let $X$ be either $A_{n-1}$ or $D_n$, and let $\theta_1^X,\ldots,\theta_n^X$ be the corresponding elements of the quadratic algebra $\Lambda_{quad}(X)$. Write $\epsilon_k$ for the…

Let $B_n$ be the Weyl group of type $B_n$. Let $\Lambda_w(B_n)$ be its left-invariant differential algebra, and let $\Lambda_{quar}(B_n)$ be the quotient of the quadratic algebra…

Let $W$ be a Weyl group, let ${\cal C}$ be its set of reflections, and let $\Lambda_w$ be the left-invariant differential algebra associated with this differential structure. Let…

An associative conformal algebra is annihilation-free if it has no nonzero annihilator, in the sense explained in the cited reference. A differential conformal algebra is an associ…

Braided Brzezinski theorem. The variant of the Brzezinski theorem for braided Hopf algebras is valid.

Let $(D,\delta,d)$ be a nonassociative differential extension as above, with $C$ the distinguished subfield of $D$ and centralizer taken in $(D,\delta,d)$. Centralizer conjecture.…