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arXiv · 1711.00416

Ringel duality for certain strongly quasi-hereditary algebras

Martin Kalck·Joseph Karmazyn
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Abstract

We introduce quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The main result is a uniform formula describing the Ringel duals of these quasi-hereditary algebras. As special cases, we obtain a Ringel-duality formula for a family of strongly quasi-hereditary algebras arising from a type A configuration of projective lines in a rational, projective surface as recently introduced by Hille and Ploog, for certain Auslander-Dlab-Ringel algebras, and for Eiriksson and Sauter's nilpotent quiver algebras when the quiver has no sinks and no sources. We also recover Tan's result that the Auslander algebras of self-injective Nakayama algebras are Ringel self-dual.

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Martin Kalck, Joseph Karmazyn. 2018-04-09. Ringel duality for certain strongly quasi-hereditary algebras. https://doi.org/10.1007/s40879-018-0250-0

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