Unbounded Operators, Lie Algebras, and Local Representations

Palle E. T. Jorgensen () and Feng Tian ()
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Palle E. T. Jorgensen: The University of Iowa, Department of Mathematics
Feng Tian: Wright State University, Department of Mathematics

Chapter 43 in Operator Theory, 2015, pp 1221-1243 from Springer

Abstract: 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.

Keywords: Riemann Surface; Unitary Representation; Local Representation; Single Operator; Unbounded Operator (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-0348-0667-1_47

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