The Gabriel-roiter Measure for Radical-square Zero Algebras
نویسنده
چکیده
Let Λ be a radical-square zero algebra over an algebraically closed field k with radical r and Γ = Λ/r 0 r Λ/r ! be the associated hereditary algebra. There is a well-known functor F : modΛ→modΓ which induces a stable equivalence. We show that the functor F keeps Gabriel-Roiter measures and Gabriel-Roiter factors. Thus one may study the Gabriel-Roiter measure for Λ using F and known facts for hereditary algebras. In particular, we study the middle terms of the almost split sequences ending at Gabriel-Roiter factor Λ-modules, and the relation between the preprojective partition for Λ and the take-off Λmodules, when Λ is of s-tame type (see section 2.3.2 for the definition).
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