Interplay between $\mathbb{Z}_2$-gradings and automorphisms in the Grassmann algebra: a survey
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908497308811264 |
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| author | Guimarães, Alan |
| author_facet | Guimarães, Alan |
| contents | Let $F$ be a field of characteristic different from two, and let $E$ be the Grassmann algebra of an infinite-dimensional $F$-vector space $L$. In this paper, we survey recent results concerning automorphisms of order two of $E$ and the corresponding induced superalgebra structures. We also present concrete examples of non-homogeneous automorphisms of $E$, as discussed in \cite{agpkauto, anagomes}. The paper concludes with a conjecture regarding the classification of the superalgebra structures of $E$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interplay between $\mathbb{Z}_2$-gradings and automorphisms in the Grassmann algebra: a survey Guimarães, Alan Rings and Algebras 15A75, 16W50, 16W55, 16R99 Let $F$ be a field of characteristic different from two, and let $E$ be the Grassmann algebra of an infinite-dimensional $F$-vector space $L$. In this paper, we survey recent results concerning automorphisms of order two of $E$ and the corresponding induced superalgebra structures. We also present concrete examples of non-homogeneous automorphisms of $E$, as discussed in \cite{agpkauto, anagomes}. The paper concludes with a conjecture regarding the classification of the superalgebra structures of $E$. |
| title | Interplay between $\mathbb{Z}_2$-gradings and automorphisms in the Grassmann algebra: a survey |
| topic | Rings and Algebras 15A75, 16W50, 16W55, 16R99 |
| url | https://arxiv.org/abs/2508.15628 |