Middle Terms of AR-sequences of Graded Kronecker Modules
Let ( T ( n ), ) be the covering of the generalized Kronecker quiver K ( n ) , where is a bipartite orientation. Then there exists a reflection functor σ on the category mod ( T ( n ), ) . Suppose that 0 → X → Y → Z → 0 is an AR-sequence in the regular component D of mod ( T ( n ), ) , and b ( Z ) is the number of flow modules in the σ -orbit of Z. Then the middle term Y is a sink (source or flow) module if and only if σ Z is a sink (source or flow) module. Moreover, their radii and centers satisfy r ( Y ) = r (σ Z ) + 1 and C ( Y ) = C (σ Z )
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