Unbounded Operators, Lie Algebras, and Local Representations

Palle E. T. Jorgensen; James Tian

doi:10.1007/978-3-032-16356-1_47

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Book chapter

Unbounded Operators, Lie Algebras, and Local Representations

Palle E. T. Jorgensen and James Tian

Operator Theory, pp.1533-1554

Springer Nature Switzerland, Second edition

2026

DOI: 10.1007/978-3-032-16356-1_47

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Abstract

Several results are presented on the integrability and extendability of Lie algebras composed of unbounded skew-symmetric operators with a common dense domain in a Hilbert space. Integrability of a Lie algebra 𝔤 𝔤 refers to the existence of an associated unitary representation U 𝓤 of the corresponding simply connected Lie group, such that U 𝓤 of the corresponding simply connected Lie group, such that 𝔤 𝔤 is the differential of U 𝓤 . The findings extend previous integrability results in the literature and introduce new insights even for the case of a single operator. Applications include the discovery of a new invariant for certain Riemann surfaces.

Harmonic Analysis

22E65

47B25

47L60

81S05

Boundary value problems

Deficiency indices

Extendability

Hilbert space

Integrability

Lie algebras

Lie groups

Local invariance

Noncommutative geometry

Riemann surfaces

Skew-symmetric operators

Spectral resolution

Unbounded operators

Unitary representations

Details

Title: Subtitle: Unbounded Operators, Lie Algebras, and Local Representations
Creators: Palle E. T. Jorgensen
James Tian
Contributors: Daniel Alpay (Editor)
Fabrizio Colombo (Editor)
Irene Sabadini (Editor)
Resource Type: Book chapter
Publication Details: Operator Theory, pp.1533-1554
Edition: Second edition
DOI: 10.1007/978-3-032-16356-1_47
Publisher: Springer Nature Switzerland; Cham
Language: English
Date published: 2026
Academic Unit: Mathematics
Record Identifier: 9985218625202771

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