Growth of Graded Twisted Calabi-Yau Algebras
| Autor: | Reyes, Manuel L., Rogalski, Daniel |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Journal of Algebra 539 (2019), 201-259 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2019.07.029 |
| Popis: | 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. Comment: 49 pages |
| Databáze: | arXiv |
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