Abstract
Birge Huisgen-Zimmermann calls a finite dimensional algebra homologically tame provided the little and the big finitistic dimension are equal and finite. The question formulated in the title has been discussed by her in the paper “Representation-tame algebras need not be homologically tame”, by looking for any r ≥ 1 at a sequence of algebras Λm with big finitistic dimension r + m. As we will show, also the little finitistic dimension of Λm is r + m. It follows that contrary to her assertion, all the algebras Λm are homologically tame.
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Huisgen-Zimmermann, B.: Representation-tame algebras need not be homologically tame. Algebras Represent. Theory 19, 943–956 (2016)
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Presented by: Christof Geiss
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Appendix: The shape of the Indecomposable Projective Λ5-Modules
Appendix: The shape of the Indecomposable Projective Λ5-Modules
These graphical displays can be found in [1]. But the referee has suggested to provide the pictures also here.
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Ringel, C.M. Are Special Biserial Algebras Homologically Tame?. Algebr Represent Theor 26, 999–1005 (2023). https://doi.org/10.1007/s10468-022-10120-x
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DOI: https://doi.org/10.1007/s10468-022-10120-x