The Simple Connectedness of a Tame Weakly Shod Algebra
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Bibliographic record
Abstract
Abstract We prove that a tame weakly shod algebra A which is not quasi-tilted is simply connected if and only if the orbit graph of its pip-bounded component is a tree, or if and only if its first Hochschild cohomology group H1(A) with coefficients in A A A vanishes. We also show that it is strongly simply connected if and only if the orbit graph of each of its directed components is a tree, or if and only if H1(A) = 0 and it contains no full convex subcategory which is hereditary of type 𝔸˜, or if and only if it is separated and contains no full convex subcategory which is hereditary of type 𝔸˜. Key Words: Tame weakly shod algebrasSimply connected and strongly simply connected algebrasOrbit graphsFirst Hochschild cohomology groupMathematics Subject Classification: 16G2016G70 Acknowledgment The authors wish to thank Diane Castonguay and Rosana Vargas for their useful comments. The first author gratefully acknowledges partial support from the NSERC of Canada. Notes #Communicated by C. Cibils.
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