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- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-011-0032-5
- Publisher site
- See Article on Publisher Site
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.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Dec 3, 2011