Number of homogeneous components of counterexamples to the Dixmier conjecture - Guccione, J.A.; Guccione, J.J.; Valqui, C. (Taylor and Francis Ltd., 2025)
Assume that P and Q are elements of A1 satisfying [𝑃,𝑄]=1. The Dixmier Conjecture for A1 says that they always generate A1. We show that if P is a sum of not more than 4 homogeneous elements of A1 then P and Q generate A1, which generalizes the main result in [Citation10].
Keywords: Mathematics; Counterexample; Conjecture; Homogeneous; Pure mathematics; Discrete mathematics; Combinatorics; https://purl.org/pe-repo/ocde/ford#1.01.01