3,127 research outputs found
On substitution algebras of permutations
The subject of this paper is a simulation to that in [1] but here we consider
substitutions corresponding to transpositions instead of replacements.Comment: arXiv admin note: substantial text overlap with arXiv:1302.304
On Galois coverings and tilting modules
Let A be a basic connected finite dimensional algebra over an algebraically
closed field, let G be a group, let T be a basic tilting A-module and let B the
endomorphism algebra of T. Under a hypothesis on T, we establish a
correspondence between the Galois coverings with group G of A and the Galois
coverings with group G of B. The hypothesis on T is expressed using the Hasse
diagram of basic tilting A-modules and is always verified if A is of finite
representation type. Then, we use the above correspondence to prove that A is
simply connected if and only if B is simply connected, under the same
hypothesis on T. Finally, we prove that if a tilted algebra B of type Q is
simply connected, then Q is a tree and the first Hochschild cohomology group of
B vanishesComment: Fourth version. A result on the simple connectedness of tilted
algebras was adde
The first Hochschild cohomology group of a schurian cluster-tilted algebra
Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã.Fil: Assem, Ibrahim. University of Sherbrooke; CanadáFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Matemática BahÃa Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática BahÃa Blanca; Argentin
Modules over cluster-tilted algebras determined by their dimension vectors
We prove that indecomposable transjective modules over cluster-tilted
algebras are uniquely determined by their dimension vectors. Similarly, we
prove that for cluster-concealed algebras, rigid modules lifting to rigid
objects in the corresponding cluster category are uniquely determined by their
dimension vectors. Finally, we apply our results to a conjecture of Fomin and
Zelevinsky on denominators of cluster variables.Comment: 9 page
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