Quotients of Incidence Algebras and the Euler Characteristic |
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| Authors: | Ibrahim Assem Diane Castonguay Sonia Trepode |
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| Institution: | 1. Département de Mathématiques , Université de Sherbrooke , Sherbrooke, Québec, Canada;2. Departamento de Matemática , IME, Universidade de S?o Paulo , S?o Paulo, Brazil;3. Departamento de Matemáticas , Universidad Nacional de Mar del Plata , Mar del Plata, Argentina |
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| Abstract: | In this note, we show that, if A ? kQ A /I A is a schurian strongly simply connected algebra given by its normed presentation, and Σ is the unique poset whose Hasse quiver coincides with Q A , then A ? kΣ if and only if I A has a generating set consisting of exactly χ(Q A ) elements, where χ(Q A ) is the Euler characteristic of Q A . We also prove that a quotient of an incidence algebra A = kΣ/J is strongly simply connected if and only if A is simply connected and kΣ is strongly simply connected. |
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| Keywords: | Euler characteristic Incidence algebras Strongly simply connected algebras |
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