Number of homogeneous components of counterexamples to the Dixmier conjecture
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910334973902848 |
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| author | Guccione, Jorge Guccione, Juan Jose Valqui, Christian |
| author_facet | Guccione, Jorge Guccione, Juan Jose Valqui, Christian |
| contents | Assume that $P$ and $Q$ are elements of $A_1$ satisfying $[P,Q] = 1$. The Dixmier Conjecture for $A_1$ says that they always generate $A_1$. We show that if $P$ is a sum of not more than~$4$ homogeneous elements of $A_1$ then $P$ and $Q$ generate $A_1$, which generalizes the main result in arXiv:2210.00257. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11135 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Number of homogeneous components of counterexamples to the Dixmier conjecture Guccione, Jorge Guccione, Juan Jose Valqui, Christian Rings and Algebras 16W20, 16S32, 16W50 Assume that $P$ and $Q$ are elements of $A_1$ satisfying $[P,Q] = 1$. The Dixmier Conjecture for $A_1$ says that they always generate $A_1$. We show that if $P$ is a sum of not more than~$4$ homogeneous elements of $A_1$ then $P$ and $Q$ generate $A_1$, which generalizes the main result in arXiv:2210.00257. |
| title | Number of homogeneous components of counterexamples to the Dixmier conjecture |
| topic | Rings and Algebras 16W20, 16S32, 16W50 |
| url | https://arxiv.org/abs/2402.11135 |