The L'vov-Kaplansky Conjecture for Polynomials of Degree Three
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918265726435328 |
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| author | Vitas, Daniel |
| author_facet | Vitas, Daniel |
| contents | The L'vov-Kaplansky conjecture states that the image of a multilinear noncommutative polynomial $f$ in the matrix algebra $M_n(K)$ is a vector space for every $n \in {\mathbb N}$. We prove this conjecture for the case where $f$ has degree $3$ and $K$ is an algebraically closed field of characteristic $0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15600 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The L'vov-Kaplansky Conjecture for Polynomials of Degree Three Vitas, Daniel Rings and Algebras 16R99, 16S50, 15A30 The L'vov-Kaplansky conjecture states that the image of a multilinear noncommutative polynomial $f$ in the matrix algebra $M_n(K)$ is a vector space for every $n \in {\mathbb N}$. We prove this conjecture for the case where $f$ has degree $3$ and $K$ is an algebraically closed field of characteristic $0$. |
| title | The L'vov-Kaplansky Conjecture for Polynomials of Degree Three |
| topic | Rings and Algebras 16R99, 16S50, 15A30 |
| url | https://arxiv.org/abs/2310.15600 |