Remarks on the Definition of a Courant Algebroid
By K. Uchino. 2002
87 citations recorded by the source corpus.
The notion of a Courant algebroid was introduced by Liu, Weinstein, and Xu in 1997. Its definition consists of five axioms and a defining relation for a derivation. It is shown that two of the axioms and the relation (assuming only the Leibniz rule) follow from the rest of the axioms.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a8b8de778125ba5cb882de5381786c3e9cbdba82
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In Algebra and Number Theory
- Y. Kosmann-Schwarzbach
- M. Gualtieri
- E. Meinrenken
- David Li-Bland
- R. Mehta
- Michel van den Bergh
- Paul Koerber
- R. Rocha
In Geometry and Topology
- E. Meinrenken
- Y. Kosmann-Schwarzbach
- David Li-Bland
- M. Gualtieri
- Anna Fino
- G. Cavalcanti
- D. Waldram
- M. Graña
In Mathematical Physics
- E. Meinrenken
- David Li-Bland
- Y. Kosmann-Schwarzbach
- M. Gualtieri
- D. Waldram
- M. Graña
- Anna Fino
- G. Cavalcanti
Citations in the corpus
- Hamiltonian Symmetries and Reduction in Generalized Geometry (2005, unknown): “In [55], it’s shown that with (6.”
- Generalized Complex Geometry (2004, background): “In [47] it is noted that this Leibniz property, together with axioms (C1) and (C5), imply not only the definition of D but also axioms (C3) and (C4).”
- Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory (2003, background): “It was further observed by Uchino [50] and by Grabowski and Marmo [19] that the number of independent conditions can be reduced.”
- Courant Algebroids and Poisson Geometry (2008, methodology): “The properties p1) and p2) are sometimes included as part of the axioms; their redundancy was first observed by Uchino [27].”