Dualizing Complexes of Noetherian Complete Algebras via Coalgebras

Author： He J.-W.   Torrecillas B.   Van Oystaeyen F.   Zhang Y.  

Publisher： Taylor & Francis Ltd

ISSN： 0092-7872

Source： Communications in Algebra, Vol.42, Iss.1, 2014-01, pp. : 271-285

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Abstract

Let A be a noetherian complete basic semiperfect algebra over an algebraically closed field, and C = A°be its dual coalgebra. If A is Artin–Schelter regular, then the local cohomology of A is isomorphic to a shift of twisted bimodule 1 C 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. An appendix is included to prove a duality theorem of the bounded derived category of quasi-finite comodules over an artinian coalgebra.

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