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



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


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
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
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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:27 Sep 2022 11:37

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