We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new
invariants including the notions of real roots and the Weyl groupoid. The crucial ingredient is …

arXiv:2308.13120v1 [math.QA] 25 Aug 2023 Page 1 arXiv:2308.13120v1 [math.QA] 25 Aug 2023
ON INFINITE-DIMENSIONAL HOPF ALGEBRAS NICOLÁS ANDRUSKIEWITSCH Dedicated to …

This is a survey on Nichols algebras of diagonal type with finite dimension, or more
generally with arithmetic root system. The knowledge of these algebras is the cornerstone of …

We give an explicit and essentially minimal list of defining relations of a Nichols algebra of
diagonal type with finite root system. This list contains the well-known quantum Serre …

Motivated by the work of Kac and Lusztig, we define a root system for a large class of
semisimple Yetter–Drinfeld modules over an arbitrary Hopf algebra which admits the …

We obtain a presentation by generators and relations of any Nichols algebra of diagonal
type with finite root system. We prove that the defining ideal is finitely generated. The proof is …

Using previous results concerning the rank two and rank three cases, all connected simply
connected Cartan schemes for which the real roots form a finite irreducible root system of …

In the structure theory of quantized enveloping algebras, the algebra isomorphisms
determined by Lusztig led to the first general construction of PBW bases of these algebras …

This paper provides some evidence for conjectural relations between extensions of (right)
weak order on Coxeter groups, closure operators on root systems, and Bruhat order. The …

We formally define and study the distinguished pre-Nichols algebra B˜ ̃ B (V) of a braided
vector space of diagonal type V with finite-dimensional Nichols algebra B (V). The algebra …