  The category of all modules over a reductive complex Lie algebra is wild, and
therefore it is useful to study full subcategories. For instance, Bernstein,
Gelfand and Gelfand introduced a category of modules which provides a natural
setting for highest weight modules. In this paper, we define a family of
categories which generalizes the BGG category, and we classify the simple
modules for a subfamily. As a consequence, we show that some of the obtained
categories are semisimple.
