Dualities of artinian coalgebras with applications to noetherian complete algebras

2010/10/06 by J. -W. He, He, J. -W., B. Torrecillas +5
Mathematics · #16E30 #16W30 #18E30 #18G10 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16E30 #msc:16W30 #msc:18E30 #msc:18G10

paper · pdf · doi:10.48550/arxiv.1010.1053

arxiv created 2010/10/06 · arxiv updated 2010/10/07

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^*A₁. If σ is an inner automorphism, then A is Calabi-Yau.

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