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Algebras and Representation Theory

, Volume 21, Issue 3, pp 605–625 | Cite as

Δ-Filtrations and Projective Resolutions for the Auslander–Dlab–Ringel Algebra

  • Teresa CondeEmail author
Article

Abstract

The ADR algebra R A of an Artin algebra A is a right ultra strongly quasihereditary algebra (RUSQ algebra). In this paper we study the Δ-filtrations of modules over RUSQ algebras and determine the projective covers of a certain class of R A -modules. As an application, we give a counterexample to a claim by Auslander–Platzeck–Todorov, concerning projective resolutions over the ADR algebra.

Keywords

Quasihereditary algebra Strongly quasihereditary algebra ADR algebra 

Mathematics Subject Classification (2010)

16S50 16W70 16G10 16G20 

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Notes

Acknowledgments

Most of this work is contained in the author’s Ph.D. thesis. This was supported by the grant SFRH/BD/84060/2012 of Fundação para a Ciência e a Tecnologia, Portugal. The author would like to express her gratitude to Stephen Donkin, Ph.D. examiner, for the simplified version of the proofs of Lemma 3.2 and Corollary 3.3 included in this article. In addition, the author would like to thank her Ph.D. supervisor, Karin Erdmann, for many useful comments.

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Institute of Algebra and Number TheoryUniversity of StuttgartStuttgartGermany

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