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On good filtration dimensions for standardly stratified algebras

Bin Zhu·S. Caenepeel
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Abstract

$\nabla$-good filtration dimensions of modules and of algebras are introduced by Parker for quasi-hereditary algebras. These concepts are now generalized to the setting of standardly stratified algebras. Let $A$ be a standardly stratified algebra. The $\bar{\nabla}$-good filtration dimension of $A$ is proved to be the projective dimension of the characteristic module of $A$. Several characterizations of $\bar{\nabla}$-good filtration dimensions and $\barΔ$-good filtration dimensions are given for properly stratified algebras. Finally we give an application of these results to the global dimensions of quasi-hereditary algebras with exact Borel subalgebra.

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Bin Zhu, S. Caenepeel. 2003-11-21. On good filtration dimensions for standardly stratified algebras. https://arxiv.org/abs/math/0209063

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