Fr ́echet Lie Algebroids and TheirCohomology

Author(s)

Fr ́echet Lie Algebroids and TheirCohomology Kaveh Eftekharinasab

We define Lie and Courant algebroids on Fr ́echetmanifolds. Moreover, we construct a Dirac structure on the gen-eralized tangent bundle of a Fr ́echet manifold and show that itinherits a Fr ́echet Lie algebroid structure. We show that the Liealgebroid cohomology of theB-cotangent bundle Lie algebroidof a weakly symplectic Fr ́echet manifoldMis the Lichnerowicz-Poisson cohomology ofM

DOI: https://armjmath.sci.am/index.php/ajm/article/view/125 Armenian Journal of Mathematics, 8(1) 77-85

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Keywords

Fr ́echet Lie algebroid, Dirac structures, Lichnerowicz-Poissoncohomology, Weak symplectic structures

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