Growth of Graded Twisted Calabi-Yau Algebras
arXiv:1808.10538 · doi:10.1016/j.jalgebra.2019.07.029
Abstract
We initiate a study of the growth and matrix-valued Hilbert series of non-negatively graded twisted Calabi-Yau algebras that are homomorphic images of path algebras of weighted quivers, generalizing techniques previously used to investigate Artin-Schelter regular algebras and graded Calabi-Yau algebras. Several results are proved without imposing any assumptions on the degrees of generators or relations of the algebras. We give particular attention to twisted Calabi-Yau algebras of dimension d at most 3, giving precise descriptions of their matrix-valued Hilbert series and partial results describing which underlying quivers yield algebras of finite GK-dimension. For d = 2, we show that these are algebras with mesh relations. For d = 3, we show that the resulting algebras are a kind of derivation-quotient algebra arising from an element that is similar to a twisted superpotential.
arXiv comment49 pages
References in corpus (6)
- Calabi-Yau algebras
- Skew Calabi-Yau Algebras and Homological Identities
- Rings graded equivalent to the Weyl algebra
- The classification of 3-dimensional noetherian cubic Calabi-Yau algebras
- Quivers supporting twisted Calabi-Yau algebras
- Generalized Gorensteinness and a homological determinant for preprojective algebras
Cited by in corpus (6)
- Graded twisted Calabi-Yau algebras are generalized Artin-Schelter regular
- Quivers supporting twisted Calabi-Yau algebras
- Isomorphisms of graded path algebras
- Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity
- Four-vertex quivers supporting twisted graded Calabi-Yau algebras
- Auslander's Theorem for dihedral actions on preprojective algebras of type A