Dualities of artinian coalgebras with applications to noetherian complete algebras

Details Dualities of artinian coalgebras with applications to noetherian complete algebras Dualities of artinian coalgebras with applications to noetherian complete algebras

2010-10-06

arxiv.org/abs/1010.1053v1

Mathematics

Rings and Algebras

Scientific paper

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 ${}_1C_{\sigma^*}$ with $\sigma$ a coalgebra automorphism. This yields that the balanced dualinzing complex of $A$ is a shift of the twisted bimodule ${}_{\sigma^*}A_1$. If $\sigma$ is an inner automorphism, then $A$ is Calabi-Yau.

Affiliated with

Also associated with

No associations

Rating

Dualities of artinian coalgebras with applications to noetherian complete algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dualities of artinian coalgebras with applications to noetherian complete algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dualities of artinian coalgebras with applications to noetherian complete algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-427127