Universidad Complutense de Madrid
E-Prints Complutense

A note on invariant operators of the Weyl algebra (Russian)

Impacto

Downloads

Downloads per month over past year



Campoamor Stursberg, Otto Ruttwig (2008) A note on invariant operators of the Weyl algebra (Russian). Matematicheskiĭ Zhurnal. Mathematical Journal , 8 (3(29)). pp. 46-51. ISSN 1682-0525



Abstract

Let L be a finite-dimensional complex Lie algebra with a basis X1,…,Xn and L∗ the dual space with a dual basis x1,…,xn. Suppose that [Xi,Xj]=∑kckijXk. Then there exists a (co)representation
Xi↦∑k,jckijxk∂∂xj
of L in the space of analytic functions on L∗. A function F is invariant if Xi∘F(x1,…,xn)=∑k,jckijxk∂∂xjF(x1,…,xn).
In the case of a pseudo-orthogonal algebra Iso(p,q) the author finds a maximal algebraically independent system of invariants C1,…,Cm consisting of Casimir operators where m=[p+q−12]. It is shown that invariants of the Weyl algebra W(p,q) have the form IJ−1, where I and J are invariants for Iso(p,q).


Item Type:Article
Additional Information:

Escrito en ruso

Uncontrolled Keywords:Coadjoint orbits; nilpotent varieties
Subjects:Sciences > Mathematics > Algebra
ID Code:22226
Deposited On:05 Jul 2013 16:47
Last Modified:12 Dec 2018 15:13

Origin of downloads

Repository Staff Only: item control page