Homological properties of homologically smooth connected cochain DGAs
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910558668718080 |
|---|---|
| author | Mao, X. -F. |
| author_facet | Mao, X. -F. |
| contents | Assume that $\mathscr{A}$ is a connected cochain DG algebra. We show that $\mathscr{A}$ is homologically smooth and Gorenstein if and only if its $\mathrm{Ext}$-algebra $H(R\Hom_{\mathscr{A}}(\mathbbm{k},\mathbbm{k}))$ is a Frobenius graded algebra. Moreover, $\mathscr{A}$ is Calabi-Yau if and only if the $\mathrm{Ext}$-algebra $H(R\Hom_{\mathscr{A}}(\mathbbm{k},\mathbbm{k}))$ is a symmetric Frobenius graded algebra. These generalize the corresponding results in \cite{HW1} and \cite{HM}, where the additional Koszul hypothesis is needed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homological properties of homologically smooth connected cochain DGAs Mao, X. -F. Rings and Algebras 16E10, 16E45, 16W50, 16E65 Assume that $\mathscr{A}$ is a connected cochain DG algebra. We show that $\mathscr{A}$ is homologically smooth and Gorenstein if and only if its $\mathrm{Ext}$-algebra $H(R\Hom_{\mathscr{A}}(\mathbbm{k},\mathbbm{k}))$ is a Frobenius graded algebra. Moreover, $\mathscr{A}$ is Calabi-Yau if and only if the $\mathrm{Ext}$-algebra $H(R\Hom_{\mathscr{A}}(\mathbbm{k},\mathbbm{k}))$ is a symmetric Frobenius graded algebra. These generalize the corresponding results in \cite{HW1} and \cite{HM}, where the additional Koszul hypothesis is needed. |
| title | Homological properties of homologically smooth connected cochain DGAs |
| topic | Rings and Algebras 16E10, 16E45, 16W50, 16E65 |
| url | https://arxiv.org/abs/2407.14805 |