Abstract
For an acyclic quiver , we solve the Clebsch–Gordan problem for the projective representations by computing the multiplicity of a given indecomposable projective in the tensor product of two indecomposable projectives. Motivated by this problem for arbitrary representations, we study idempotents in the representation ring of (the free abelian group on the indecomposable representations, with multiplication given by tensor product). We give a general technique for constructing such idempotents and for decomposing the representation ring into a direct product of ideals, utilizing morphisms between quivers and categorical Möbius inversion.
Citation
Ryan Kinser. Ralf Schiffler. "Idempotents in representation rings of quivers." Algebra Number Theory 6 (5) 967 - 994, 2012. https://doi.org/10.2140/ant.2012.6.967
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