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Unbounded Operators, Lie Algebras, and Local Representations

In: Operator Theory

Author

Listed:
  • Palle E. T. Jorgensen

    (The University of Iowa, Department of Mathematics)

  • Feng Tian

    (Wright State University, Department of Mathematics)

Abstract

A number Unbounded operators of results on integrability and extendability of Lie algebras of unbounded skew-symmetric operators with common dense domain in Hilbert space are proved. By integrability for a Lie algebra 𝔤 $$\mathfrak{g}$$ , it means that there is an associated unitary representation 𝒰 $$\mathcal{U}$$ of the corresponding simply connected Lie group such that 𝔤 $$\mathfrak{g}$$ is the differential of 𝒰 $$\mathcal{U}$$ . The results extend earlier integrability results in the literature and are new even in the case of a single operator. Applications include a new invariant for certain Riemann surfaces.

Suggested Citation

  • Palle E. T. Jorgensen & Feng Tian, 2015. "Unbounded Operators, Lie Algebras, and Local Representations," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 43, pages 1221-1243, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_47
    DOI: 10.1007/978-3-0348-0667-1_47
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