Abstract
We study the simple connectedness of the class of finite-dimensional algebras over an algebraically closed field for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. We show that a tame algebra in this class is simply connected if and only if its first Hochschild cohomology space vanishes.
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I thank an anonymous referee for useful comments.
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Presented by: Christof Geiss
Dedicated to Claus Michael Ringel on the occasion of his 75th birthday
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Malicki, P. The Simple Connectedness of Tame Algebras with Separating Almost Cyclic Coherent Auslander–Reiten Components. Algebr Represent Theor 25, 923–951 (2022). https://doi.org/10.1007/s10468-021-10053-x
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DOI: https://doi.org/10.1007/s10468-021-10053-x
Keywords
- Simply connected algebra
- Hochschild cohomology
- Auslander–Reiten quiver
- Tame algebra
- Generalized multicoil algebra