Andruskiewitsch–Schneider generation conjecture for finite Nichols algebras

Let K=kGK=\Bbbk G for a finite group GG, and let

R=n0RnKKYDR=\bigoplus_{n\ge 0}R^n\in{}^{K}_{K}\mathcal{YD}

be a finite-dimensional coradically graded connected Hopf algebra, with R1R^1 its degree-one component. Andruskiewitsch–Schneider conjecture. RR is generated as an algebra by R1R^1; equivalently,

R=B(R1).R=\mathcal{B}(R^1).

This is the generation-in-degree-one step of the Andruskiewitsch–Schneider lifting method for classifying finite-dimensional pointed Hopf algebras. The source gives no resolution status for the conjecture.

Sources & referencesView supporting material

Primary source

Iván Angiono, “Pointed Hopf algebras revisited, with a view from tensor categories”, arXiv:2510.03124 (2026).

Additional references

7 papers in this index state this conjecture (2001–2025). The statement above is taken from the most recent of them; the others are arXiv:1705.00339, arXiv:1701.01991, arXiv:1612.04987, arXiv:1403.7838, arXiv:1008.4144, arXiv:math/0110136.

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