國立清華大學 數學系

Abstract:
‭Two weeks ago, we discussed the modular class of a Poisson manifold, which characterizes the obstruction to the existence of a volume form invariant under Hamiltonian vector fields. Since a Poisson manifold naturally gives rise to a Lie algebroid, we may wonder whether the modular class can be studied within the framework of Lie algebroids. In this talk, I will begin with a fundamental introduction to Lie algebroids, followed by the definition of their modular classes. After that, we will explore some examples and revisit the case of Poisson manifolds.