LÉvy洛伦兹-李代数的过程

Pub Date : 2023-11-01 DOI:10.1142/9789811275999_0003

Ameur Dhahri, Uwe Franz

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引用次数: 0

摘要

研究了Lorentz群李代数上Schurmann意义上的Levy过程。已知在洛伦兹群的不可约酉表示中，只有一个存在非平凡的一环。构造了该循环的Schurmann三重体，并研究了相关Levy过程的性质。描述了这个三元组的约束分解为李子代数$so(3)$和$so(2,1)$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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LÉVY PROCESSES ON THE LORENTZ-LIE ALGEBRA

Levy processes in the sense of Schurmann on the Lie algebra of the Lorentz grouop are studied. It is known that only one of the irreducible unitary representations of the Lorentz group admits a non-trivial one-cocycle. A Schurmann triple is constructed for this cocycle and the properties of the associated Levy process are investigated. The decommpositions of the restrictions of this triple to the Lie subalgebras $so(3)$ and $so(2,1)$ are described.

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