  The notion of gluing of abelian categories was introduced by Kazhdan and
Laumon in an attempt of another geometric construction of representations of
finite Chevalley groups; the approach was later developed by Polishchuk and
Braverman. We observe that this notion of gluing is a particular case of a
general categorical construction (used also by Kontsevich and Rosenberg to
define "noncommutative schemes"). We prove a conjecture of Kazhdan which says
that the D-module counterpart of the Kazhdan-Laumon gluing construction
produces a category equivalent to modules over the ring $\mathcal D$ of global
differential operators on the basic affine space. As an application we show
that $\mathcal D$ is Noetherian, and has finite injective dimension as a module
over itself.
