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arXiv · 1406.6966

Unbounded operators, Lie algebras, and local representations

Palle Jorgensen·Feng Tian
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Abstract

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

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Palle Jorgensen, Feng Tian. 2014-06-26. Unbounded operators, Lie algebras, and local representations. https://arxiv.org/abs/1406.6966

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