Hecke-Hopf algebras

Arkady Berenstein; David Kazhdan

doi:10.1016/j.aim.2019.06.018

Hecke-Hopf algebras

Arkady Berenstein^*, David Kazhdan

^*Corresponding author for this work

Einstein Institute of Mathematics

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

3 Scopus citations

Abstract

Let W be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras H_q(W) as (left) coideal subalgebras. Our Hecke-Hopf algebras¹ H(W) have a number of applications. In particular they provide new solutions of quantum Yang-Baxter equation and lead to a construction of a new family of endo-functors of the category of H_q(W)-modules. Hecke-Hopf algebras for the symmetric group are related to Fomin-Kirillov algebras; for an arbitrary Coxeter group W the “Demazure” part of H(W) is being acted upon by generalized braided derivatives which generate the corresponding (generalized) Nichols algebra.

Original language	English
Pages (from-to)	312-395
Number of pages	84
Journal	Advances in Mathematics
Volume	353
DOIs	https://doi.org/10.1016/j.aim.2019.06.018
State	Published - 7 Sep 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Coideal
Hecke algebra
Hopf algebra

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10.1016/j.aim.2019.06.018

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title = "Hecke-Hopf algebras",

abstract = "Let W be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras Hq(W) as (left) coideal subalgebras. Our Hecke-Hopf algebras1 H(W) have a number of applications. In particular they provide new solutions of quantum Yang-Baxter equation and lead to a construction of a new family of endo-functors of the category of Hq(W)-modules. Hecke-Hopf algebras for the symmetric group are related to Fomin-Kirillov algebras; for an arbitrary Coxeter group W the “Demazure” part of H(W) is being acted upon by generalized braided derivatives which generate the corresponding (generalized) Nichols algebra.",

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AU - Berenstein, Arkady

AU - Kazhdan, David

PY - 2019/9/7

Y1 - 2019/9/7

N2 - Let W be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras Hq(W) as (left) coideal subalgebras. Our Hecke-Hopf algebras1 H(W) have a number of applications. In particular they provide new solutions of quantum Yang-Baxter equation and lead to a construction of a new family of endo-functors of the category of Hq(W)-modules. Hecke-Hopf algebras for the symmetric group are related to Fomin-Kirillov algebras; for an arbitrary Coxeter group W the “Demazure” part of H(W) is being acted upon by generalized braided derivatives which generate the corresponding (generalized) Nichols algebra.

AB - Let W be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras Hq(W) as (left) coideal subalgebras. Our Hecke-Hopf algebras1 H(W) have a number of applications. In particular they provide new solutions of quantum Yang-Baxter equation and lead to a construction of a new family of endo-functors of the category of Hq(W)-modules. Hecke-Hopf algebras for the symmetric group are related to Fomin-Kirillov algebras; for an arbitrary Coxeter group W the “Demazure” part of H(W) is being acted upon by generalized braided derivatives which generate the corresponding (generalized) Nichols algebra.

KW - Coideal

KW - Hecke algebra

KW - Hopf algebra

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AN - SCOPUS:85068995406

SN - 0001-8708

VL - 353

SP - 312

EP - 395

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Hecke-Hopf algebras

Abstract

Bibliographical note

Keywords

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