Simple Jordan superalgebras with the even parts of Clifford type
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909533891198976 |
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| author | Shestakov, Ivan Zelmanov, Efim |
| author_facet | Shestakov, Ivan Zelmanov, Efim |
| contents | The purpose of this paper is a partial progress towards classification of simple infinite dimensional Jordan superalgebras. First, we prove that the only simple infinite dimensional Jordan superalgebras with finite dimensional even parts are the superalgebras of superforms. Then we consider the superalgebras whose even parts are infinite dimensional algebras of ``Clifford type'', that is, direct sums of algebras of bilinear forms. The results of \cite{RZ} show that the number of summonds in these sums is 1 or 2. We prove that the second case is impossible and that the simple infinite dimensional Jordan superalgebras of the first type are the superalgebras of superforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple Jordan superalgebras with the even parts of Clifford type Shestakov, Ivan Zelmanov, Efim Rings and Algebras Primary 17A70, 16W10, Secondary 17C70, 16W55 The purpose of this paper is a partial progress towards classification of simple infinite dimensional Jordan superalgebras. First, we prove that the only simple infinite dimensional Jordan superalgebras with finite dimensional even parts are the superalgebras of superforms. Then we consider the superalgebras whose even parts are infinite dimensional algebras of ``Clifford type'', that is, direct sums of algebras of bilinear forms. The results of \cite{RZ} show that the number of summonds in these sums is 1 or 2. We prove that the second case is impossible and that the simple infinite dimensional Jordan superalgebras of the first type are the superalgebras of superforms. |
| title | Simple Jordan superalgebras with the even parts of Clifford type |
| topic | Rings and Algebras Primary 17A70, 16W10, Secondary 17C70, 16W55 |
| url | https://arxiv.org/abs/2503.08164 |