Abstract
Dlab and Ringel showed that algebras being quasi-hereditary in all orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary. As a matter of fact, we consider permutations of indices, and if the algebra with permuted indices is quasi-hereditary, then we say that this permutation gives quasi-heredity. In this article, we give a criterion for adjacent transpositions giving quasi-heredity, in terms of homological conditions of standard or costandard modules over a given quasi-hereditary algebra.
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Acknowledgements
I would like to thank prof. Katsuhiro Uno for many helpful discussions with him and improving this article. I am also grateful to Takahide Adachi, Aaron Chan, Yuta Kimura and Mayu Tsukamoto for their valuable comments and discussions. I wish also to thank the referee for giving me a lot of advice.
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Goto wrote all the manuscript.
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Presented by: Henning Krause
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Goto, Y. Criterion for Quasi-Heredity. Algebr Represent Theor (2024). https://doi.org/10.1007/s10468-024-10263-z
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DOI: https://doi.org/10.1007/s10468-024-10263-z