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On the Orbit Method for the Lie Algebra of Vector Fields on a Curve

✍ Scribed by Rosane Ushirobira

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
326 KB
Volume
203
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let α’„ be the Lie algebra of vector fields on an affine smooth curve ⌺. Our goal is to establish an orbit method for α’„. Since α’„ is infinite-dimensional, we face some technical problems. Without having groups acting on α’„, we try nevertheless to define the notion of ''orbits.'' So, we focus our attention to a subspace α’„ U of α’„ U . f This subspace consists of the ''finite-dimensional orbits.'' To almost all in α’„ U it f corresponds a simple induced representation of α’„ whose annihilator is a primitive ideal. We conjecture that this ideal has a finite Gelfand᎐Kirillov codimension. Ε½ What we are actually looking for is a bijection similar to Dixmier's bijection in the .

U finite-dimensional case between the ''orbits'' of α’„ and certain primitive ideals of f the enveloping algebra of α’„.

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