Geodesic
A Remark on the Dixmier Conjecture
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 6-12

Voir la notice de l'article provenant de la source Cambridge University Press

The Dixmier Conjecture says that every endomorphism of the (first) Weyl algebra $A_{1}$ (over a field of characteristic zero) is an automorphism, i.e., if $PQ-QP=1$ for some $P,Q\in A_{1}$, then $A_{1}=K\langle P,Q\rangle$. The Weyl algebra $A_{1}$ is a $\mathbb{Z}$-graded algebra. We prove that the Dixmier Conjecture holds if the elements $P$ and $Q$ are sums of no more than two homogeneous elements of $A_{1}$ (there is no restriction on the total degrees of $P$ and $Q$).
DOI : 10.4153/S0008439519000122
Mots-clés : Weyl algebra, Dixmier Conjecture, automorphism, endomorphism, a Z-graded algebra 
Bavula, V. V.; Levandovskyy, V. A Remark on the Dixmier Conjecture. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 6-12. doi: 10.4153/S0008439519000122
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