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arXiv · 2506.20395

Embedding theorems as a bridge between supertraces and supergeometry

Charles Almeida·Lucio Centrone·Claudemir Fideles
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Abstract

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 $A\otimes\Xi$, where $\Xi$ 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.

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Charles Almeida, Lucio Centrone, Claudemir Fideles. 2025-06-25. Embedding theorems as a bridge between supertraces and supergeometry. https://arxiv.org/abs/2506.20395

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