The type C rack conjecture for finite Nichols algebras

Let O\mathcal{O} be a finite rack of type C, let q\mathfrak{q} be a faithful 22-cocycle on O\mathcal{O}, and let B(O,q)\mathscr{B}(\mathcal{O},\mathfrak{q}) denote the associated Nichols algebra. Type C rack conjecture. Then

GK-dimB(O,q)=\operatorname{GK-dim}\mathscr{B}(\mathcal{O},\mathfrak{q})=\infty

for every faithful 22-cocycle q\mathfrak{q}. The conjecture predicts infinite growth for Nichols algebras arising from finite racks of type C and is part of the program classifying finite-Gelfand–Kirillov-dimensional Nichols algebras.

Sources & referencesView supporting material

Primary source

Nicolás Andruskiewitsch, “On infinite-dimensional Hopf algebras”, arXiv:2308.13120 (2023).

Additional references

2 papers in this index state this conjecture (2021–2023). The statement above is taken from the most recent of them; the others are arXiv:2104.04789.

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