The fundamental groups of a triangular algebra |
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| Authors: | Ibrahim Assem José Antonio de la Peña |
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| Institution: | 1. Departement de Mathématiques et Informatique , Université de Sherbrooke Sherbrooke , Québec, J1K 2R1, Canada E-mail: ibrahim. assem@dmi.usherb.ca;2. Institute de Matemáticas , Universidad Nacional , México 04510, Autónoma de México, D.F, México E-mail: joseant@redvaxl.dgsca.unam.mx |
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| Abstract: | A finite dimensional algebra A (over an algebraically closed field) is called triangular if its ordinary quiver has no oriented cycles. To each presentation (Q I) of A is attached a fundamental group π1(Q I), and A is called simply connected if π1(Q I) is trivial for every presentation of A. In this paper, we provide tools for computations with the fundamental groups, as well as criteria for simple connectedness. We find relations between the fundamental groups of A and the first Hochschild cohomology H 1 (A A). |
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| Keywords: | Algebraic curve Linear series Line bundle Gonality Projectively normal Normal generation |
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