?Anti-commutable? local pre-Leibniz algebroids and admissible connections

dc.authoridDogan, Keremcan/0000-0001-7071-8585en_US
dc.contributor.authorDereli, Tekin
dc.contributor.authorDogan, Keremcan
dc.date.accessioned2024-07-12T21:37:30Z
dc.date.available2024-07-12T21:37:30Z
dc.date.issued2023en_US
dc.department[Belirlenecek]en_US
dc.description.abstractThe concept of algebroid is convenient as a basis for constructions of geometrical frameworks. For example, metric-affine and generalized geometries can be written on Lie and Courant algebroids, respectively. Furthermore, string theories might make use of many other algebroids such as metric algebroids, higher Courant algebroids, or conformal Courant algebroids. Working on the possibly most general algebroid structure, which generalizes many of the algebroids used in the literature, is fruitful as it creates a chance to study all of them at once. Local pre-Leibniz algebroids are such general ones in which metric-connection geometries are possible to construct. On the other hand, the existence of the 'locality operator', which is present for the left-Leibniz rule for the bracket, necessitates the modification of torsion and curvature operators in order to achieve tensorial quantities. In this paper, this modification of torsion and curvature is explained from the point of view that the modification is applied to the bracket instead. This leads one to consider 'anti-commutable' local pre-Leibniz algebroids which satisfy an anti-commutativity-like property defined with respect to a choice of an equivalence class of connections. These 'admissible' connections are claimed to be the necessary ones while working on a geometry of algebroids. This claim is due to the fact that one can prove many desirable properties and relations if one uses only admissible connections. For instance, for admissible connections, we prove the first and second Bianchi identities, Cartan structure equations, Cartan magic formula, the construction of Levi-Civita connections, the decomposition of connection in terms of torsion and non-metricity. These all are possible because the modified bracket becomes anti-symmetric for an admissible connection so that one can apply the machinery of almost-or pre-Lie algebroids. We investigate various algebroid structures from the literature and show that they admit admissible connections which are metric-compatible in some generalized sense. Moreover, we prove that local pre-Leibniz algebroids that are not anti-commutable cannot be equipped with a torsion-free, and in particular Levi-Civita, connection. (c) 2023 Elsevier B.V. All rights reserved.en_US
dc.description.sponsorshipIstanbul Technical University BAP Postdoctoral Research Fellowship (DOSAP) [TAB-2021-43202]; Turkish Academy of Sciences (TUBA)en_US
dc.description.sponsorshipThe authors are thankful to Cem Yetismisoğlu for long and fruitful discussions on many details of this work. The authors are also grateful to the anonymous referee for their valuable contributions. KD is funded by Istanbul Technical University BAP Postdoctoral Research Fellowship (DOSAP) with project number TAB-2021-43202. TD thanks the Turkish Academy of Sciences (TUBA) for partial support.en_US
dc.identifier.doi10.1016/j.geomphys.2023.104752
dc.identifier.issn0393-0440
dc.identifier.issn1879-1662
dc.identifier.scopus2-s2.0-85149741024en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1016/j.geomphys.2023.104752
dc.identifier.urihttps://hdl.handle.net/20.500.12415/6816
dc.identifier.volume186en_US
dc.identifier.wosWOS:000932521700001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofJournal of Geometry And Physicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmzKY04158
dc.subjectPre-Leibniz Algebroidsen_US
dc.subjectAdmissible Connectionsen_US
dc.subjectBianchi Identitiesen_US
dc.subjectCartan Formalismen_US
dc.subjectLie Algebroidsen_US
dc.subjectGeneralized Geometryen_US
dc.title?Anti-commutable? local pre-Leibniz algebroids and admissible connectionsen_US
dc.typeArticle
dspace.entity.typePublication

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