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- W4292939155 abstract "In this thesis, we discuss relationship between resolution quivers of cyclic Nakayama algebra $Lambda$ and the associated algebra $epsilon(Lambda)$ defined by E.Sen. We will show that if $Lambda$ is cyclic Nakayama algebra of infinite global dimension, then resolution quiver of $epsilon(Lambda)$ embeds in that of $Lambda$ as subquiver; and this embedding preserves weight of cycles. From this result, we give an explicit formula of $phi$-$dim(Lambda)$ by relating $phi$-$dim$ to a geometrical quantity of resolution quiver $R(Lambda)$. We can use the result concerning resolution quiver embedding to characterize all resolution quivers of basic connected Nakayama algebras. Then we will use $phi$-$dim$ formula to compute $phi$-$dim$ of a two parameter family of cyclic Nakayama algebras having infinite global dimension, and check that its $phi$-$dim$ attains every even integer. At the end, we will use a graphical method to determine whether $gl$-$dim(Lambda)$ is infinite. Using this graphical construction, we can show any cyclic Nakayama algebra with minimum length of indecomposable projective modules greater than the number of vertices, must have infinite global dimension: we show this by iteratively producing modules of infinite projective dimension.--Author's abstract" @default.
- W4292939155 created "2022-08-24" @default.
- W4292939155 creator A5045575199 @default.
- W4292939155 date "2022-08-24" @default.
- W4292939155 modified "2023-10-03" @default.
- W4292939155 title "Resolution quivers of epsilon constructions and characterization of resolution quivers of cyclic nakayama algebra" @default.
- W4292939155 doi "https://doi.org/10.17760/d20439226" @default.
- W4292939155 hasPublicationYear "2022" @default.
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