The Lie algebra Vec(ℝ) of polynomial vector fields on the line acts naturally on ℂ[]. This action has a one-parameter family of deformations called the tensor density modules F_λ. The bounded indecomposable modules of Vec(ℝ) of length 2 composed of tensor density modules have been classified by Feigin and Fuchs. We present progress towards describing the annihilators of the unique indecomposable extension of F_λ by F_(λ+2) in the non-resonant case λ ≠ -½. We give the intersection of the annihilator and the subalgebra of lowest weight vectors of the universal enveloping algebra (Vec(ℝ)) of Vec(ℝ). This result is found by applying structural descriptions of the lowest weight vectors of (Vec(ℝ)).
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc1505233 |
| Date | 05 1900 |
| Creators | Kenefake, Tyler Christian |
| Contributors | Conley, Charles, Cherry, William, 1966-, Shepler, Anne |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 37 pages, Text |
| Rights | Public, Kenefake, Tyler Christian, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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