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

2022/12/15 by Angiono, Iván, Iglesias, Agustín García · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2212.08169

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 \mathfrakB(V) is finite if and only if the corresponding root system is finite, that is \mathfrakB(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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