A Remark on the Constructibility of Real Root Representations of Quivers Using Universal Extension Functors
نویسنده
چکیده
Let k be a field and let Q be a (finite) quiver. We fix a representation S with EndkQ S = k and Ext 1 kQ(S, S) = 0. In analogy to [3, Section 1] we consider the following subcategories of repk Q. Let M S be the full subcategory of all modules X with ExtkQ(S,X) = 0 such that, in addition, X has no direct summand which can be embedded into some direct sum of copies of S. Similarly, let MS be the full subcategory of all modules X with ExtkQ(X,S) = 0 such that, in addition, no direct summand of X is a quotient of a direct sum of copies of S. Finally, let M be the full subcategory of all modules X with HomkQ(X,S) = 0, and let M−S be the full subcategory of all modules X with HomkQ(S,X) = 0. Moreover, we consider
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