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Lie Groups and Representation Theory
Seminar information archive ～04/24｜Next seminar｜Future seminars 04/25～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|
2008/05/13
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
加藤晃史 (東京大学)
On endomorphisms of the Weyl algebra
http://akagi.ms.u-tokyo.ac.jp/seminar.html
加藤晃史 (東京大学)
On endomorphisms of the Weyl algebra
[ Abstract ]
Noncommutative geometry has revived the interest in the Weyl algebras, which are basic building blocks of quantum field theories.
The Weyl algebra $A_n(\\C)$ is an associative algebra over $\\C$ generated by $p_i, q_i$ ($i=1,\\cdots,n$) with relations $[p_i, q_j]=\\delta_{ij}$. Every endomorphism of $A_n$ is injective since $A_n$ is simple.
Dixmier (1968) initiated a systematic study of the Weyl algebra $A_1$ and posed the following problem: Is every endomorphism of $A_1$ an automorphism?
We give an affirmative answer to this conjecture.
[ Reference URL ]Noncommutative geometry has revived the interest in the Weyl algebras, which are basic building blocks of quantum field theories.
The Weyl algebra $A_n(\\C)$ is an associative algebra over $\\C$ generated by $p_i, q_i$ ($i=1,\\cdots,n$) with relations $[p_i, q_j]=\\delta_{ij}$. Every endomorphism of $A_n$ is injective since $A_n$ is simple.
Dixmier (1968) initiated a systematic study of the Weyl algebra $A_1$ and posed the following problem: Is every endomorphism of $A_1$ an automorphism?
We give an affirmative answer to this conjecture.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
