A note on stable equivalence and Nakayama algebras
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Abstract:
Two artin algebras $\Lambda$ and $\Lambda ’$ are said to be stably equivalent if the categories of finitely generated modules modulo projective for $\Lambda$ and $\Lambda ’$ are equivalent categories. If $\Lambda ’$ is stably equivalent to a Nakayama (i.e. generalized uniserial) algebra $\Lambda$, we prove that $\Lambda$ and $\Lambda ’$ have the same number of nonprojective simple modules. And if $\Lambda$ and $\Lambda ’$ are stably equivalent indecomposable Nakayama algebras where each indecomposable projective module has length at least 3, then $\Lambda$ and $\Lambda ’$ have the same admissible sequences.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 71 (1978), 157-163
- MSC: Primary 16A46; Secondary 16A35, 16A64
- DOI: https://doi.org/10.1090/S0002-9939-1978-0500481-7
- MathSciNet review: 500481