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E6(6) exceptional Drinfel’d algebras

Emanuel Malek Orcid Logo, Yuho Sakatani, Daniel Thompson Orcid Logo

Journal of High Energy Physics, Volume: 2021, Issue: 1

Swansea University Author: Daniel Thompson Orcid Logo

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DOI (Published version): 10.1007/jhep01(2021)020

Abstract

The exceptional Drinfel’d algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence, it provides an M-theoretic analogue of the way a Drinfel’d double encodes generalised T-dualities of strings. I...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: Springer Science and Business Media LLC 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa60618
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first_indexed 2022-07-25T09:54:19Z
last_indexed 2023-01-13T19:20:52Z
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spelling 2022-10-25T14:31:45.6693079 v2 60618 2022-07-25 E6(6) exceptional Drinfel’d algebras 9c8715ee44a574eda1194c9808d99c62 0000-0001-8319-8275 Daniel Thompson Daniel Thompson true false 2022-07-25 SPH The exceptional Drinfel’d algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence, it provides an M-theoretic analogue of the way a Drinfel’d double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is E6(6). We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold G, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel’d doubles and others that are not of this type. Journal Article Journal of High Energy Physics 2021 1 Springer Science and Business Media LLC 1029-8479 Flux compactifications, M-Theory, String Duality, Superstring Vacua 5 1 2021 2021-01-05 10.1007/jhep01(2021)020 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University SCOAP3 2022-10-25T14:31:45.6693079 2022-07-25T10:52:06.1732552 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Emanuel Malek 0000-0003-0196-3610 1 Yuho Sakatani 2 Daniel Thompson 0000-0001-8319-8275 3 60618__24728__307fc2acf984439ca6630d6ddab1c1c8.pdf 60618.pdf 2022-07-25T10:54:08.1939476 Output 564055 application/pdf Version of Record true Copyright: The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0) true eng https://creativecommons.org/licenses/by/4.0/
title E6(6) exceptional Drinfel’d algebras
spellingShingle E6(6) exceptional Drinfel’d algebras
Daniel Thompson
title_short E6(6) exceptional Drinfel’d algebras
title_full E6(6) exceptional Drinfel’d algebras
title_fullStr E6(6) exceptional Drinfel’d algebras
title_full_unstemmed E6(6) exceptional Drinfel’d algebras
title_sort E6(6) exceptional Drinfel’d algebras
author_id_str_mv 9c8715ee44a574eda1194c9808d99c62
author_id_fullname_str_mv 9c8715ee44a574eda1194c9808d99c62_***_Daniel Thompson
author Daniel Thompson
author2 Emanuel Malek
Yuho Sakatani
Daniel Thompson
format Journal article
container_title Journal of High Energy Physics
container_volume 2021
container_issue 1
publishDate 2021
institution Swansea University
issn 1029-8479
doi_str_mv 10.1007/jhep01(2021)020
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description The exceptional Drinfel’d algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence, it provides an M-theoretic analogue of the way a Drinfel’d double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is E6(6). We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold G, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel’d doubles and others that are not of this type.
published_date 2021-01-05T04:18:52Z
_version_ 1763754254243201024
score 11.014067

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