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arXiv · 1010.1053

Dualities of artinian coalgebras with applications to noetherian complete algebras

J. -W. He·B. Torrecillas·F. Van Oystaeyen·Y. Zhang
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Abstract

A duality theorem of the bounded derived category of quasi-finite comodules over an artinian coalgebra is established. Let $A$ be a noetherian complete basic semiperfect algebra over an algebraically closed field, and $C$ be its dual coalgebra. If $A$ is Artin-Schelter regular, then the local cohomology of $A$ is isomorphic to a shift of twisted bimodule ${}_1C_{σ^*}$ with $σ$ a coalgebra automorphism. This yields that the balanced dualinzing complex of $A$ is a shift of the twisted bimodule ${}_{σ^*}A_1$. If $σ$ is an inner automorphism, then $A$ is Calabi-Yau.

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J. -W. He, B. Torrecillas, F. Van Oystaeyen, Y. Zhang. 2010-10-06. Dualities of artinian coalgebras with applications to noetherian complete algebras. https://arxiv.org/abs/1010.1053

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