AR-Components of domestic finite group schemes: McKay-Quivers and Ramification

DOI10.1093/QMATH/HAX043zbMATH Open1423.16014arXiv1512.04821OpenAlexW2962970040MaRDI QIDQ4684210

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Publication date: 27 September 2018

Published in: (Search for Journal in Brave)

Abstract: For a domestic finite group scheme, we give a direct description of the Euclidean components in its Auslander-Reiten quiver via the McKay-quiver of a finite linearly reductive subgroup scheme of $SL(2)$. Moreover, for a normal subgroup scheme $mathcalN$ of a finite group scheme $mathcalG$, we show that there is a connection between the ramification indices of the restriction morphism $mathbbP(mathcal{V}_{mathcalN})ightarrowmathbbP(mathcal{V}_{mathcalG})$ between their projectivized cohomological support varieties and the ranks of the tubes in their Auslander-Reiten quivers.

Full work available at URL: https://arxiv.org/abs/1512.04821

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