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Volume 29, Issue 5 (Sep 2017)

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Some homological properties of category 𝒪. IV

Kevin Coulembier
  • Corresponding author
  • School of Mathematics and Statistics, University of Sydney, NSW 2006, Sydney, Australia; and Department of Mathematical Analysis, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
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/ Volodymyr Mazorchuk
Published Online: 2016-09-20 | DOI: https://doi.org/10.1515/forum-2016-0108

Abstract

We study projective dimension and graded length of structural modules in parabolic-singular blocks of the BGG category 𝒪. Some of these are calculated explicitly, others are expressed in terms of two functions. We also obtain several partial results and estimates for these two functions and relate them to monotonicity properties for quasi-hereditary algebras. The results are then applied to study blocks of 𝒪 in the context of Guichardet categories, in particular, we show that blocks of 𝒪 are not always weakly Guichardet.

Keywords: Projective dimension; graded length; quasi-hereditary algebra

MSC 2010: 16E30; 17B10

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About the article


Received: 2016-04-30

Revised: 2016-08-09

Published Online: 2016-09-20

Published in Print: 2017-09-01


The first author is Postdoctoral Fellow of the Research Foundation – Flanders (FWO). The second author is partially supported by the Swedish Research Council.


Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2016-0108.

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