Equivalence classes of subquotients of pseudodifferential operator modules
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- by Charles H. Conley and Jeannette M. Larsen PDF
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Abstract:
Consider the spaces of pseudodifferential operators between tensor density modules over the line as modules of the Lie algebra of vector fields on the line. We compute the equivalence classes of various subquotients of these modules. There is a 2-parameter family of subquotients with any given Jordan-Hölder composition series. In the critical case of subquotients of length 5, the equivalence classes within each non-resonant 2-parameter family are specified by the intersections of a pencil of conics with a pencil of cubics. In the case of resonant subquotients of length 4 with self-dual composition series, as well as in those of lacunary subquotients of lengths 3 and 4, equivalence is specified by a single pencil of conics. Non-resonant subquotients of length exceeding 7 admit no non-obvious equivalences. The cases of lengths 6 and 7 are unresolved.References
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Additional Information
- Charles H. Conley
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- Email: conley@unt.edu
- Jeannette M. Larsen
- Affiliation: Department of Mathematics, University of Texas at Tyler, Tyler, Texas 75799
- Email: jlarsen@uttyler.edu
- Received by editor(s): June 9, 2013
- Received by editor(s) in revised form: January 28, 2014
- Published electronically: December 10, 2014
- Additional Notes: The first author was partially supported by Simons Foundation Collaboration Grant 207736.
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 8809-8842
- MSC (2010): Primary 17B66
- DOI: https://doi.org/10.1090/S0002-9947-2014-06428-3
- MathSciNet review: 3403072