Vanishing theorems on Kähler Lie algebroids.

In this paper, we extend the Hodge theory to complex Lie algebroids, introduce the Laplacian operators and decompose the cohomological groups with respect to these operators, and generalize Kahler and Nakano identities to Kähler Lie algebroids as well. Our main purpose is to extend Kodaira vanishing theorem to Kahler Lie algebroids. [ABSTRACT FROM AUTHOR]