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

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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.

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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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  1. Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Teresa Conde

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  1. Teresa Conde
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Correspondence to Teresa Conde.

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Presented by Vlastimil Dlab.

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Conde, T. Δ-Filtrations and Projective Resolutions for the Auslander–Dlab–Ringel Algebra. Algebr Represent Theor 21, 605–625 (2018). https://doi.org/10.1007/s10468-017-9730-z

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