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arXiv · 2301.13041

Pre-Nichols algebras of one-parameter families of finite Gelfand-Kirillov dimension

Emiliano Campagnolo
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Abstract

Between the braided vector spaces of diagonal type there exist some families whose associated Nichols algebras are infinite dimensional but with finite Gelfand-Kirillov dimension, called one-parameter families. We show that every pre-Nichols algebra of finite Gelfand-Kirillov dimension of this kind with connected diagram is necessarily the corresponding Nichols algebra, up to few exceptions. For each one of these exceptions we present a proper pre-Nichols algebra by generators and relations, and prove that it is the corresponding eminent pre-Nichols algebra. This paper essentially ends the determination of the eminent pre-Nichols algebras of diagonal type, the first step towards the classification of pre-Nichols algebras of diagonal type with finite GKdim.

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Emiliano Campagnolo. 2023-01-30. Pre-Nichols algebras of one-parameter families of finite Gelfand-Kirillov dimension. https://arxiv.org/abs/2301.13041

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