arXiv 0909.32792009-09-17math.QA

Pohlmeyer-Schwarren Poisson代数的拟李双代数表示

A quasi-Lie bialgebra formulation of the Pohlmeyer-Rehren Poisson algebra

Martin Bordemann, Benjamin Enriquez, Laurent Hofer

备注：: 8 pages, proceedings of the Poisson geometry 2006 conference
发表信息：: Travaux mathematiques. Vol. XVII, 87--100, Trav. Math., 17, Fac. Sci. Technol. Commun. Univ. Luxemb., Luxembourg, 2007

摘要：

我们提出了一个准李双代数（QLBA）的量子化问题，它来自于一个代数的重组Nambu-Goto弦理论和不变的费用Pohlmeyer和Rehren。这种QLBA结构依赖于对称双向量（来自Minkowski度量），并建立在有限维向量空间上的自由李代数上。我们解决这个问题时，双向量的秩为1或2。

英文摘要：

We present a quasi-Lie bialgebra (QLBA) quantization problem which comes from an algebraic reformulation of the Nambu-Goto string theory and invariant charges by Pohlmeyer and Rehren. This QLBA structure depends on a symmetric bivector (coming from a Minkowski metric) and is built on the free Lie algebra on a finite dimensional vector space. We solve this problem when the bivector has rank 1 or 2.

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