On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra

Details On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra

2011-01-22

arxiv.org/abs/1101.4305v2

Mathematics

Rings and Algebras

16 pages

Scientific paper

Let $A_1=K < X, Y | [Y,X]=1>$ be the (first) Weyl algebra over a field $K$ of characteristic zero. It is known that the set of eigenvalues of the inner derivation $\ad (YX)$ of $A_1$ is $\Z$. Let $ A_1\ra A_1$, $X\mapsto x$, $Y\mapsto y$, be a $K$-algebra homomorphism, i.e. $[y,x]=1$. It is proved that the set of eigenvalues of the inner derivation $\ad (yx)$ of the Weyl algebra $A_1$ is $\Z$ and the eigenvector algebra of $\ad (yx)$ is $K< x,y> $ (this would be an easy corollary of the Problem/Conjecture of Dixmier of 1968 [still open]: {\em is an algebra endomorphism of $A_1$ an automorphism?}).

Affiliated with

Also associated with

No associations

Rating

On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-643897