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arXiv · 2608.03299

Comparing self-dual corings, Frobenius corings and Ringel self-duality

Tomasz Brzeziński·Teresa Conde·Steffen Koenig·Julian Külshammer
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Abstract

Self-dual corings and self-dual algebra extensions are classified and these (self-)dualities are compared with Ringel (self-)duality, revealing fundamental differences. To each coring $\mathcal C$, two algebras are associated, known as the left and the right dual algebra of $\mathcal C$. It is shown that these two algebras coincide in a natural way if and only if $\mathcal C$ is a Frobenius coring. Various other equivalent characterisations of $\mathcal C$ being self-dual are given, in terms of certain algebra extensions being Frobenius extensions and in terms of certain forgetful or restriction functors being Frobenius functors. Ringel self-duality however is shown to be rather different, for which a homological explanation is given.

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Tomasz Brzeziński, Teresa Conde, Steffen Koenig, Julian Külshammer. 2026-08-04. Comparing self-dual corings, Frobenius corings and Ringel self-duality. https://arxiv.org/abs/2608.03299

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