Fr\'echet Lie algebroids and their cohomology
Kaveh Eftekharinasab

TL;DR
This paper extends the concepts of Lie and Courant algebroids to Fréchet manifolds, constructs Dirac structures, and relates their cohomology to known Poisson cohomology, broadening geometric analysis in infinite-dimensional settings.
Contribution
It introduces Fréchet Lie and Courant algebroids, constructs Dirac structures on them, and links their cohomology to Lichnerowicz-Poisson cohomology, advancing the theory in infinite-dimensional geometry.
Findings
Defined Lie and Courant algebroids on Fréchet manifolds
Constructed Dirac structures on generalized tangent bundles
Connected Lie algebroid cohomology to Lichnerowicz-Poisson cohomology
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 -cotangent bundle Lie algebroid of a weakly symplectic Fr\'{e}chet manifold is the Lichnerowicz-Poisson cohomology of .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons · Advanced Topics in Algebra
