Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras
In this paper, we investigate the Koszul behavior of finitely semi-graded algebras by the distributivity of some associated lattice of ideals. The Hilbert series, the Poincaré series, and the Yoneda algebra are defined for this class of algebras. Moreover, the point modules and the point fu...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-07-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/11/7/881 |
| _version_ | 1818039144148893696 |
|---|---|
| author | Oswaldo Lezama Jaime Gomez |
| author_facet | Oswaldo Lezama Jaime Gomez |
| author_sort | Oswaldo Lezama |
| collection | DOAJ |
| description | In this paper, we investigate the Koszul behavior of finitely semi-graded algebras by the distributivity of some associated lattice of ideals. The Hilbert series, the Poincaré series, and the Yoneda algebra are defined for this class of algebras. Moreover, the point modules and the point functor are introduced for finitely semi-graded rings. Finitely semi-graded algebras and rings include many important examples of non-<inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">N</mi> </semantics> </math> </inline-formula>-graded algebras coming from mathematical physics that play a very important role in mirror symmetry problems, and for these concrete examples, the Koszulity will be established, as well as the explicit computation of its Hilbert and Poincaré series. |
| first_indexed | 2024-12-10T07:53:57Z |
| format | Article |
| id | doaj.art-93b6de8f61734ecd916e973674e36be6 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-12-10T07:53:57Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-93b6de8f61734ecd916e973674e36be62022-12-22T01:56:58ZengMDPI AGSymmetry2073-89942019-07-0111788110.3390/sym11070881sym11070881Koszulity and Point Modules of Finitely Semi-Graded Rings and AlgebrasOswaldo Lezama0Jaime Gomez1Seminario de Álgebra Constructiva-SAC<sup>2</sup>, Departamento de Matemáticas, Universidad Nacional de Colombia, Sede Bogotá 111321, ColombiaSeminario de Álgebra Constructiva-SAC<sup>2</sup>, Departamento de Matemáticas, Universidad Nacional de Colombia, Sede Bogotá 111321, ColombiaIn this paper, we investigate the Koszul behavior of finitely semi-graded algebras by the distributivity of some associated lattice of ideals. The Hilbert series, the Poincaré series, and the Yoneda algebra are defined for this class of algebras. Moreover, the point modules and the point functor are introduced for finitely semi-graded rings. Finitely semi-graded algebras and rings include many important examples of non-<inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">N</mi> </semantics> </math> </inline-formula>-graded algebras coming from mathematical physics that play a very important role in mirror symmetry problems, and for these concrete examples, the Koszulity will be established, as well as the explicit computation of its Hilbert and Poincaré series.https://www.mdpi.com/2073-8994/11/7/881graded algebrasdistributive latticesKoszul algebrasHilbert and Poincaré seriesYoneda algebrapoint modulespoint functorZariski topologyskew PBW extensions |
| spellingShingle | Oswaldo Lezama Jaime Gomez Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras Symmetry graded algebras distributive lattices Koszul algebras Hilbert and Poincaré series Yoneda algebra point modules point functor Zariski topology skew PBW extensions |
| title | Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras |
| title_full | Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras |
| title_fullStr | Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras |
| title_full_unstemmed | Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras |
| title_short | Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras |
| title_sort | koszulity and point modules of finitely semi graded rings and algebras |
| topic | graded algebras distributive lattices Koszul algebras Hilbert and Poincaré series Yoneda algebra point modules point functor Zariski topology skew PBW extensions |
| url | https://www.mdpi.com/2073-8994/11/7/881 |
| work_keys_str_mv | AT oswaldolezama koszulityandpointmodulesoffinitelysemigradedringsandalgebras AT jaimegomez koszulityandpointmodulesoffinitelysemigradedringsandalgebras |