Hopf algebras on decorated noncrossing arc diagrams

Vincent Pilaud

doi:10.1016/j.jcta.2018.09.005

Hopf algebras on decorated noncrossing arc diagrams

Vincent Pilaud

Research output: Contribution to journal › Article › peer-review

Abstract

Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general method to endow these objects with Hopf algebra structures. Specific instances of this method produce relevant Hopf algebras that appeared earlier in the literature.

Original language	English
Pages (from-to)	486-507
Number of pages	22
Journal	Journal of Combinatorial Theory. Series A
Volume	161
DOIs	https://doi.org/10.1016/j.jcta.2018.09.005
Publication status	Published - 1 Jan 2019

Keywords

Hopf algebras
Lattice congruences
Non-crossing arc diagrams
Weak order

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10.1016/j.jcta.2018.09.005

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title = "Hopf algebras on decorated noncrossing arc diagrams",

abstract = "Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general method to endow these objects with Hopf algebra structures. Specific instances of this method produce relevant Hopf algebras that appeared earlier in the literature.",

keywords = "Hopf algebras, Lattice congruences, Non-crossing arc diagrams, Weak order",

author = "Vincent Pilaud",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

month = jan,

day = "1",

doi = "10.1016/j.jcta.2018.09.005",

language = "English",

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AU - Pilaud, Vincent

PY - 2019/1/1

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N2 - Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general method to endow these objects with Hopf algebra structures. Specific instances of this method produce relevant Hopf algebras that appeared earlier in the literature.

AB - Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general method to endow these objects with Hopf algebra structures. Specific instances of this method produce relevant Hopf algebras that appeared earlier in the literature.

KW - Hopf algebras

KW - Lattice congruences

KW - Non-crossing arc diagrams

KW - Weak order

U2 - 10.1016/j.jcta.2018.09.005

DO - 10.1016/j.jcta.2018.09.005

M3 - Article

AN - SCOPUS:85053776345

SN - 0097-3165

VL - 161

SP - 486

EP - 507

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

ER -

Hopf algebras on decorated noncrossing arc diagrams

Abstract

Keywords

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