49 research outputs found
Cyclic -algebras and double Poisson algebras
In this article we prove that there exists an explicit bijection between nice
-pre-Calabi-Yau algebras and -double Poisson differential graded
algebras, where , extending a result proved by N. Iyudu and
M. Kontsevich. We also show that this correspondence is functorial in a quite
satisfactory way, giving rise to a (partial) functor from the category of
-double Poisson dg algebras to the partial category of -pre-Calabi-Yau
algebras. Finally, we further generalize it to include double
-algebras, as introduced by T. Schedler.Comment: 27 pages. All comments are welcome
Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions
In this article we prove derived invariance of Hochschild-Mitchell homology
and cohomology and we extend to -linear categories a result by Barot and
Lenzing concerning derived equivalences and one-point extensions.
We also prove the existence of a Happel long exact sequence and we give a
generalization of this result which provides an alternative approach.Comment: 17 page