Book chapter
Unbounded Operators, Lie Algebras, and Local Representations
Operator Theory, pp.1221-1243
Springer Basel
06/20/2015
DOI: 10.1007/978-3-0348-0667-1_47
Abstract
A numberUnbounded 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\documentclass[12pt]{minimal}
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\begin{document}$$\mathfrak{g}$$\end{document}, it means that there is an associated unitary representation 𝒰\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{U}$$\end{document} of the corresponding simply connected Lie group such that 𝔤\documentclass[12pt]{minimal}
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\begin{document}$$\mathfrak{g}$$\end{document} is the differential of 𝒰\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{U}$$\end{document}. 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.
Details
- Title: Subtitle
- Unbounded Operators, Lie Algebras, and Local Representations
- Creators
- Palle E. T Jorgensen - University of IowaFeng Tian - Wright State University
- Resource Type
- Book chapter
- Publication Details
- Operator Theory, pp.1221-1243
- DOI
- 10.1007/978-3-0348-0667-1_47
- Publisher
- Springer Basel; Basel
- Language
- English
- Date published
- 06/20/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9984240868302771
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