Extended Curvatures and Lie Algebroids

Extended Curvatures and Lie Algebroids

The aim of the paper is to find conditions in which the derived almost Lie vector bundle E1 of an almost Lie vector bundle E is a Lie algebroid. The conditions are that some extended curvatures on E, considered in the paper, are vanishing. Two non-trivial examples are given. One example is when E0 i...

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Veröffentlicht in:Symmetry (Basel) 2022-07, Vol.14 (7), p.1375
Hauptverfasser: Popescu, Marcela, Popescu, Paul
Format: Artikel
Sprache:eng
Schlagworte:
almost Lie vector bundle
Jacobiator
Lie algebroid
skew symmetric algebroid
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Beschreibung
Zusammenfassung:The aim of the paper is to find conditions in which the derived almost Lie vector bundle E1 of an almost Lie vector bundle E is a Lie algebroid. The conditions are that some extended curvatures on E, considered in the paper, are vanishing. Two non-trivial examples are given. One example is when E0 is a skew symmetric algebroid; the other one is when E1 is not a skew symmetric algebroid.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14071375