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Dirac–Nijenhuis structures

J Clemente-Gallardo, J M Nunes da Costa
2004 Journal of Physics A: Mathematical and General  
In this paper we study the concept of Dirac-Nijenhuis structures. We consider them to be a pair (D, N ) where D is a Dirac structure, defined with respect to a Lie bialgebroid (A, A * ), and N is a Nijenhuis operator which defines a deformation of the Lie algebroid structure of D in a compatible way. The transformation can be considered to deform also the double of the Lie bialgebroid, which leads to the concept of Dirac-Nijenhuis structures of type I, or to not affect it, leading to
more » ... ading to Dirac-Nijenhuis structures of type II. We prove that the concept contains Poisson-Nijenhuis structures as a particular case and provides another example for the case of Kähler manifolds.
doi:10.1088/0305-4470/37/29/007 fatcat:ffs7gn6yjbfptlhdvwdi4stqdq