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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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