Armenian Journal of Mathematics

Fr\'{e}chet Lie Algebroids and Their Cohomology

Eftekharinasab, Kaveh (2016) Fr\'{e}chet Lie Algebroids and Their Cohomology. Armenian Journal of Mathematics, 8 (1). pp. 77-85. ISSN 1829-1163

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Abstract

We define Lie and Courant algebroids on Fr\'{e}chet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Fr\'{e}chet manifold and show that it inherits a Fr\'{e}chet Lie algebroid structure. We show that the Lie algebroid cohomology of the $\bb$-cotangent bundle Lie algebroid of a weakly symplectic Fr\'{e}chet manifold $M$ is the Lichnerowicz-Poisson cohomology of $M$.

Item Type:Article
Uncontrolled Keywords:Fr\'{e}chet Lie algebroid, Dirac structures, Lichnerowicz-Poisson cohomology, Weak symplectic structures
Subjects:53-xx Differential geometry
55-xx Algebraic topology
58-xx Global analysis, analysis on manifolds
ID Code:652
Deposited By:Dr. Kaveh Eftekharinasab
Deposited On:07 Jun 2016 17:19
Last Modified:07 Jun 2016 17:19

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