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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.20395 |
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| _version_ | 1866915358511726592 |
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| author | Almeida, Charles Centrone, Lucio Fideles, Claudemir |
| author_facet | Almeida, Charles Centrone, Lucio Fideles, Claudemir |
| contents | Any algebra herein is intended over a field of characteristic 0. Let $E$ denote the infinite dimensional Grassman algebra. Given a power associative finite dimensional {$\mathbb{Z}_2$-graded-central-simple} $A$ and a supertrace algebra $B$, so that $B$ belongs to the same variety of $A\otimes E$, we study conditions on $B$ so that it can be embedded into $A\otimesΞ$, where $Ξ$ is a supercommutative algebra, called $A$-universal supermap of $B$, provided $B$ satisfies all the supertrace identities of $A\otimes E$. We use this result in order to relate the formal smoothness of $B$ with that of its $A$-universal supermap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embedding theorems as a bridge between supertraces and supergeometry Almeida, Charles Centrone, Lucio Fideles, Claudemir Rings and Algebras 16R30, 16W55, 17A05, 17A50, 14L15 Any algebra herein is intended over a field of characteristic 0. Let $E$ denote the infinite dimensional Grassman algebra. Given a power associative finite dimensional {$\mathbb{Z}_2$-graded-central-simple} $A$ and a supertrace algebra $B$, so that $B$ belongs to the same variety of $A\otimes E$, we study conditions on $B$ so that it can be embedded into $A\otimesΞ$, where $Ξ$ is a supercommutative algebra, called $A$-universal supermap of $B$, provided $B$ satisfies all the supertrace identities of $A\otimes E$. We use this result in order to relate the formal smoothness of $B$ with that of its $A$-universal supermap. |
| title | Embedding theorems as a bridge between supertraces and supergeometry |
| topic | Rings and Algebras 16R30, 16W55, 17A05, 17A50, 14L15 |
| url | https://arxiv.org/abs/2506.20395 |