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arXiv · 2402.11135

Number of homogeneous components of counterexamples to the Dixmier conjecture

Jorge Guccione·Juan Jose Guccione·Christian Valqui
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Abstract

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.

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Jorge Guccione, Juan Jose Guccione, Christian Valqui. 2024-02-16. Number of homogeneous components of counterexamples to the Dixmier conjecture. https://arxiv.org/abs/2402.11135

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