Yangians as Pre-Lie and Tridendriform Algebras

Anastasia Doikou

doi:10.1007/978-3-031-62407-0_18

Yangians as Pre-Lie and Tridendriform Algebras

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Based on the rigorous discrete derivations of Dyson series and the Magnus expansion, key links between quantum algebras, tridendriform and pre-Lie algebras are established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras actions.

Original language	English
Title of host publication	Geometric Methods in Physics XL
Editors	Piotr Kielanowski, Daniel Beltita, Alina Dobrogowska, Tomasz Goliński
Publisher	Springer
Pages	233-250
Number of pages	18
ISBN (Electronic)	9783031624070
ISBN (Print)	9783031624063
DOIs	https://doi.org/10.1007/978-3-031-62407-0_18
Publication status	Published - 27 May 2024
Event	XL Workshop on Geometric Methods in Physics 2023 - Białowieża, Poland Duration: 26 Jun 2023 → 30 Jun 2023 https://wgmp.uwb.edu.pl/plakaty/40.jpg

Publication series

Name	Trends in Mathematics
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Conference

Conference	XL Workshop on Geometric Methods in Physics 2023
Abbreviated title	WGMP 2023
Country/Territory	Poland
City	Białowieża
Period	26/06/23 → 30/06/23
Internet address	https://wgmp.uwb.edu.pl/plakaty/40.jpg

Keywords

Discrete Magnus expansion
Pre-Lie and tridendriform algebras
Yangian
Coproducts

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10.1007/978-3-031-62407-0_18

Cite this

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title = "Yangians as Pre-Lie and Tridendriform Algebras",

abstract = "Based on the rigorous discrete derivations of Dyson series and the Magnus expansion, key links between quantum algebras, tridendriform and pre-Lie algebras are established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras actions.",

keywords = "Discrete Magnus expansion, Pre-Lie and tridendriform algebras, Yangian, Coproducts",

author = "Anastasia Doikou",

year = "2024",

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doi = "10.1007/978-3-031-62407-0_18",

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AB - Based on the rigorous discrete derivations of Dyson series and the Magnus expansion, key links between quantum algebras, tridendriform and pre-Lie algebras are established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras actions.

KW - Discrete Magnus expansion

KW - Pre-Lie and tridendriform algebras

KW - Yangian

KW - Coproducts

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M3 - Conference contribution

SN - 9783031624063

T3 - Trends in Mathematics

SP - 233

EP - 250

BT - Geometric Methods in Physics XL

A2 - Kielanowski, Piotr

A2 - Beltita, Daniel

A2 - Dobrogowska, Alina

A2 - Goliński, Tomasz

PB - Springer

T2 - XL Workshop on Geometric Methods in Physics 2023<br/>

Y2 - 26 June 2023 through 30 June 2023

ER -

Yangians as Pre-Lie and Tridendriform Algebras

Abstract

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Conference

Keywords

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