In this note, we investigate how different fundamental groups of presentations of a fixed algebra A can be. For finitely many finitely presented groups Gi, we construct an algebra A such that all Gi appear as fundamental groups of presentations of A.
In this paper, we define concepts of crowns and quasi-crowns, valid in an arbitrary schurian algebra, and which generalise the corresponding concepts in an incidence algebra. We show first that a triangular schurian algebra is strongly simply connected if and only if it is simply connected and contains no quasi-crown. We then prove that the absence of quasi-crowns in a triangular schurian algebra implies the existence of a multiplicative basis.
A proposta deste trabalho consiste em uma solução aproximada para o problema do subgrafo planar de peso máximo (WMPG Weighted Maximal Planar Graph). O algoritmo baseia-se na adição de vértices, aproveitando-se da construção de triangulações nas faces do grafo. A vantagem do uso deste algoritmo dá-se pelo fato que todo grafo gerado por ele é maximal planar, descartando a necessidade de um teste de planaridade. Apresentamos um algoritmo sequencial e um paralelo para o problema WMPG e suas respectivas implementações. Os resultados obtidos com a versão paralela executando em uma arquitetura manycore, com instâncias de até 85 vértices, apresentaram speedups de até 107 vezes em relação à solução sequencial.
In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of the module category. We describe the Auslander-Reiten components of an ada algebra, showing in particular that its representation theory is entirely contained in that of its left and right supports, which are both tilted algebras. Also, we prove that an ada algebra over an algebraically closed field is simply connected if and only if its first Hochschild cohomology group vanishes.
In this note, we consider an algebra A which is a one-point extension of another algebra B and we study the morphism of fundamental groups induced by the inclusion of (the bound quiver of) B into (that of) A. Our main result says that the cokernel of this morphism is a free group and we prove some consequences from this fact. Subject classification : 16G20.
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