Rigid modules over preprojective algebras |
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Authors: | Christof Geiß Bernard Leclerc Jan Schröer |
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Affiliation: | 1. Instituto de Matemáticas, UNAM, Ciudad Universitaria, 04510, Mexico D.F., Mexico 2. Laboratoire LMNO, Université de Caen, F-14032, Caen Cedex, France 3. Mathematisches Institut, Universit?t Bonn, Beringstr. 1, D-53115, Bonn, Germany
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Abstract: | Let Λ be a preprojective algebra of simply laced Dynkin type Δ. We study maximal rigid Λ-modules, their endomorphism algebras and a mutation operation on these modules. This leads to a representation-theoretic construction of the cluster algebra structure on the ring ℂ[N] of polynomial functions on a maximal unipotent subgroup N of a complex Lie group of type Δ. As an application we obtain that all cluster monomials of ℂ[N] belong to the dual semicanonical basis. Mathematics Subject Classification (2000) 14M99, 16D70, 16E20, 16G20, 16G70, 17B37, 20G42 |
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