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

DOI

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
@article{10_4153_S0008439519000122,
     author = {Bavula, V. V. and Levandovskyy, V.},
     title = {A {Remark} on the {Dixmier} {Conjecture}},
     journal = {Canadian mathematical bulletin},
     pages = {6--12},
     year = {2020},
     volume = {63},
     number = {1},
     doi = {10.4153/S0008439519000122},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000122/}
}
TY  - JOUR
AU  - Bavula, V. V.
AU  - Levandovskyy, V.
TI  - A Remark on the Dixmier Conjecture
JO  - Canadian mathematical bulletin
PY  - 2020
SP  - 6
EP  - 12
VL  - 63
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000122/
DO  - 10.4153/S0008439519000122
ID  - 10_4153_S0008439519000122
ER  - 
%0 Journal Article
%A Bavula, V. V.
%A Levandovskyy, V.
%T A Remark on the Dixmier Conjecture
%J Canadian mathematical bulletin
%D 2020
%P 6-12
%V 63
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000122/
%R 10.4153/S0008439519000122
%F 10_4153_S0008439519000122

Cité par Sources :