A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems

Angiono, Iván Ezequiel. "A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems." Journal of the European Mathematical Society 017.10 (2015): 2643-2671. <http://eudml.org/doc/277571>.

@article{Angiono2015,
abstract = {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 based on Kharchenko’s theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.},
author = {Angiono, Iván Ezequiel},
journal = {Journal of the European Mathematical Society},
keywords = {Nichols algebras; quantized enveloping algebras; pointed Hopf algebras; Nichols algebras; convex orders},
language = {eng},
number = {10},
pages = {2643-2671},
publisher = {European Mathematical Society Publishing House},
title = {A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems},
url = {http://eudml.org/doc/277571},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Angiono, Iván Ezequiel
TI - A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 10
SP - 2643
EP - 2671
AB - 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 based on Kharchenko’s theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.
LA - eng
KW - Nichols algebras; quantized enveloping algebras; pointed Hopf algebras; Nichols algebras; convex orders
UR - http://eudml.org/doc/277571
ER -