TL;DR
This paper investigates homological regularity phenomena in category O and its variants, focusing on projective dimensions of twisted and shuffled modules, contributing to the understanding of homological properties in representation theory.
Contribution
It introduces new results on homological regularity and computes projective dimensions for specific modules in category O and its generalizations.
Findings
Homological regularity phenomena characterized in category O
Projective dimensions of twisted modules determined
Results extend to variants and generalizations of category O
Abstract
This paper explores various homological regularity phenomena (in the sense of Auslander) in category and its several variations and generalizations. Additionally, we address the problem of determining projective dimension of twisted and shuffled projective and tilting modules.
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