NDLI: Nijenhuis structures on Courant algebroids

Content Provider	Springer Nature Link
Author	Kosmann Schwarzbach, Yvette
Copyright Year	2011
Abstract	We study Nijenhuis structures on Courant algebroids in terms of the canonical Poisson bracket on their symplectic realizations. We prove that the Nijenhuis torsion of a skew-symmetric endomorphism N of a Courant algebroid is skewsymmetric if N 2 is proportional to the identity, and only in this case when the Courant algebroid is irreducible. We derive a necessary and sufficient condition for a skewsymmetric endomorphism to give rise to a deformed Courant structure. In the case of the double of a Lie bialgebroid (A, A*), given an endomorphism N of A that defines a skew-symmetric endomorphism N of the double of A, we prove that the torsion ofN is the sum of the torsion of N and that of the transpose of N.
Ending Page	649
Page Count	25
Starting Page	625
File Format	PDF
ISSN	16787544
e-ISSN	16787714
Journal	Bulletin of the Brazilian Mathematical Society
Issue Number	4
Volume Number	42
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-12-03
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Poisson algebras Lie algebroids Nijenhuis torsion Courant algebroids generalized tangent bundle Lie bialgebras; Lie coalgebras Theoretical, Mathematical and Computational Physics Mathematics Poisson manifolds; Poisson groupoids and algebroids Generalized geometries (Ã¡ la Hitchin) deformations of structures
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Nijenhuis structures on Courant algebroids