Editing Lie algebra representation (section)

==Infinite-dimensional representations and "category O"==
Let <math>\mathfrak{g}</math> be a finite-dimensional semisimple Lie algebra over a field of characteristic zero. (in the solvable or nilpotent case, one studies [[primitive ideal]]s of the enveloping algebra; cf. Dixmier for the definitive account.)

The category of (possibly infinite-dimensional) modules over <math>\mathfrak{g}</math> turns out to be too large especially for homological algebra methods to be useful: it was realized that a smaller subcategory [[category O]] is a better place for the representation theory in the semisimple case in zero characteristic. For instance, the category O turned out to be of a right size to formulate the celebrated BGG reciprocity.{{CN|date=November 2023}}