Large annihilator category [formula omitted] for [formula omitted].

We construct a new analogue of the BGG category O for the infinite-dimensional Lie algebras g = sl (∞) , o (∞) , sp (∞). A main difference with the categories studied in [9] and [2] is that all objects of our category satisfy the large annihilator condition introduced in [5]. Despite the fact that the splitting Borel subalgebras b of g are not conjugate, one can eliminate the dependency on the choice of b and introduce a universal highest weight category OLA of g -modules, the letters LA coming from "large annihilator". The subcategory of integrable objects in OLA is precisely the category T g studied in [5]. We investigate the structure of OLA , and in particular compute the multiplicities of simple objects in standard objects and the multiplicities of standard objects in indecomposable injectives. We also complete the annihilators in U (g) of simple objects of OLA. [ABSTRACT FROM AUTHOR]