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

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 10, page 2643-2671
- ISSN: 1435-9855

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topAngiono, 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 -

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