Abstract. We begin the study of a tilting theory in certain truncated categories of modu-les G(Γ) for the current Lie algebra associated to a finite-dimensional complex simple Lie algebra, where Γ = P+ × J, J is an interval in Z, and P+ is the set of dominant integral weights of the simple Lie algebra. We use this to put a tilting theory on the category G(Γ′) where Γ ′ = P ′×J, where P ′ ⊆ P+ is saturated. Under certain natural conditions on Γ′, we note that G(Γ′) admits full tilting modules. Key words: current algebra; tilting module; Serre subcategory 2010 Mathematics Subject Classification: 17B70; 17B65; 17B10; 17B55
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