4 problems

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Colmenarejo–Morales–Panova conjecture on PBW coefficients
Let $w$ be a monomial in the down-up algebra $\mathcal{P}$ , and let $\mathscr{S}$ be its PBW basis of staircase monomials. Write the expansion of $w$ in the basis $\mathscr{S}$ , an…
Conjectureopenalgebraic-combinatorics down-up-algebrasarXiv posted 2 days ago
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Rigidity of graded noetherian down-up algebras under semisimple Hopf algebra actions
Rigidity conjecture. The graded noetherian down-up algebras are rigid with respect to semisimple Hopf algebra actions.
Conjectureopendown-up-algebras hopf-algebras noncommutative-algebraarXiv posted 2 days ago
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Algebra grading conjecture for generalized uniform-poset algebras
The generalized grading conjecture. The corresponding algebra $S$ has a direct-sum algebra grading
Conjectureopenalgebra-gradings down-up-algebras uniform-posetsarXiv posted 2 days ago
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Augmented down-up algebra grading conjecture for $\hat{\mathbb T}$
The grading conjecture. The degree-zero component has basis
Conjectureopenalgebra-gradings down-up-algebras noncommutative-algebraarXiv posted 2 days ago

Colmenarejo–Morales–Panova conjecture on PBW coefficients