Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915153768873984 |
|---|---|
| author | Holleben, Thiago Nicklasson, Lisa |
| author_facet | Holleben, Thiago Nicklasson, Lisa |
| contents | Inspired by the Roller Coaster Theorem from graph theory, we prove the existence of artinian Gorenstein algebras with unconstrained Hilbert series, which we call Roller Coaster algebras. Our construction relies on Nagata idealization of quadratic monomial algebras defined by whiskered graphs. The monomial algebras are interesting in their own right, as our results suggest that artinian level algebras defined by quadratic monomial ideals rarely have the weak Lefschetz property. In addition, we discover a large family of G-quadratic Gorenstein algebras failing the weak Lefschetz property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property Holleben, Thiago Nicklasson, Lisa Commutative Algebra Combinatorics 13E10, 13H10, 13F55, 05C31 Inspired by the Roller Coaster Theorem from graph theory, we prove the existence of artinian Gorenstein algebras with unconstrained Hilbert series, which we call Roller Coaster algebras. Our construction relies on Nagata idealization of quadratic monomial algebras defined by whiskered graphs. The monomial algebras are interesting in their own right, as our results suggest that artinian level algebras defined by quadratic monomial ideals rarely have the weak Lefschetz property. In addition, we discover a large family of G-quadratic Gorenstein algebras failing the weak Lefschetz property. |
| title | Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property |
| topic | Commutative Algebra Combinatorics 13E10, 13H10, 13F55, 05C31 |
| url | https://arxiv.org/abs/2502.00155 |