In English tradition, LITERATURE usually is not used with A
It is definitely possible to precede "literature" with an indefinite article ("a"). English has a literature. It is called "English literature".
"It has been remarked that the tendency of literature in all countries today is towards what is called realism, or that method which deals with human life and action as it is rather than as it should be, as under the method of the purely romantic. This is especially true of the literature of Germany, of France, of Russia, and of America — if we can properly say that America has a literature."
"Yet when we turn to Taoism, we find that this too has a literature of its own — a most remarkable literature, and a most remarkable history."
"The result shows that Kanarese has a literature of vast extent, reaching back till its beginnings are lost in the mists of time."
"In 1919 George Abraham Grierson wrote that Kashmiri is the only one of the Dardic languages that has a literature."