Calabi-Yau Frobenius algebras

Details Calabi-Yau Frobenius algebras Calabi-Yau Frobenius algebras

2007-10-18

arxiv.org/abs/0710.3391v3

Mathematics

Rings and Algebras

39 pages; v3 has several corrections and some reorganization

Scientific paper

We define Calabi-Yau and periodic Frobenius algebras over arbitrary base commutative rings. We define a Hochschild analogue of Tate cohomology, and show that the "stable Hochschild cohomology" of periodic CY Frobenius algebras has a Batalin-Vilkovisky and Frobenius algebra structure. Such algebras include (centrally extended) preprojective algebras of (generalized) Dynkin quivers, and group algebras of classical periodic groups. We use this theory to compute (for the first time) the Hochschild cohomology of many algebras related to quivers, and to simplify the description of known results. Furthermore, we compute the maps on cohomology from extended Dynkin preprojective algebras to the Dynkin ones, which relates our CY property (for Frobenius algebras) to that of Ginzburg (for algebras of finite Hochschild dimension).

Affiliated with

Also associated with

No associations

Rating

Calabi-Yau Frobenius 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 Calabi-Yau Frobenius algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Calabi-Yau Frobenius algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-460490