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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
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 |
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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: | 27 Sep 2022 11:37 |
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