Calabi-Yau Frobenius algebras
By Ching-Hwa Eu, Travis Schedler. 2007
48 citations recorded by the source corpus.
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).
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fa456f5a043d1f65a289c880a118ed20b0dda3b8
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Citations in the corpus
- The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra (2014, background): “Tradler showed that the Hochschild cohomology algebra of a symmetric algebra is a BV algebra [32], see also [12][28].”
- Periodic resolutions and self-injective algebras of finite type (2008, methodology): “ Galois cover, smash product, stable Auslander algebra. 1 Recently there has been renewed interest in periodicity questions arising from the study of Calabi-Yau dimensions of stable module categories [5, 13, 16], and we apply our results to calculate these dimensions for the standard symmetric algeb”
- On the Hochschild cohomology ring of tensor products of algebras (2014, background): “For different proofs of this fact, see [13] and [3].”
- Batalin-Vilkovisky algebra structures on Hochschild Cohomology (2007, background): “The last proof, the proof of Eu et Schedler [8] looks similar to ours.”