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Finite GK-dimensional Nichols algebras of diagonal type and finite root systems

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arxiv 2212.08169 v1 pith:OTZM7IYW submitted 2022-12-15 math.QA

Iván Angiono , Agustín García Iglesias This is my paper · ORCID
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abstract

Let $(V,c)$ be a finite-dimensional braided vector space of diagonal type. We show that the Gelfand Kirillov dimension of the Nichols algebra $\mathfrak{B}(V)$ is finite if and only if the corresponding root system is finite, that is $\mathfrak{B}(V)$ admits a PBW basis with a finite number of generators. This had been conjectured in arXiv:1606.02521 and proved for $\dim V=2,3$ in arXiv:1803.08804, arXiv:2106.10143 respectively.

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  1. Computing finite Weyl groupoids

    math.RT 2025-05 conditional novelty 4.0 of 10

    Explicit algorithms compute the finite generalized root systems of diagonal-type Nichols algebras and contragredient Lie superalgebras, together with the Lyndon words and hyperwords of their PBW bases.

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