On graded and shifted notions, and thick morphisms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912480535511040 |
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| author | Voronov, Theodore |
| author_facet | Voronov, Theodore |
| contents | We consider the notions of $L_{\infty}$-, $P_{\infty}$-, and $S_{\infty}$-algebras (including "shifted" versions) in the $\mathbb{Z}_2 \times \mathbb{Z}$-graded setting. We also consider thick (microformal) morphisms and show how they work in such graded context.
In particular, we show that a "shifted $S_{\infty}$-thick morphism" (which we introduce here) induces an $L_{\infty}$-morphism of shifted $S_{\infty}$-structures. The same holds for "shifted $P_{\infty}$-thick morphisms" and shifted $P_{\infty}$-structures, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On graded and shifted notions, and thick morphisms Voronov, Theodore Rings and Algebras Mathematical Physics Differential Geometry Quantum Algebra We consider the notions of $L_{\infty}$-, $P_{\infty}$-, and $S_{\infty}$-algebras (including "shifted" versions) in the $\mathbb{Z}_2 \times \mathbb{Z}$-graded setting. We also consider thick (microformal) morphisms and show how they work in such graded context. In particular, we show that a "shifted $S_{\infty}$-thick morphism" (which we introduce here) induces an $L_{\infty}$-morphism of shifted $S_{\infty}$-structures. The same holds for "shifted $P_{\infty}$-thick morphisms" and shifted $P_{\infty}$-structures, respectively. |
| title | On graded and shifted notions, and thick morphisms |
| topic | Rings and Algebras Mathematical Physics Differential Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2506.16920 |