Projective unitary positive-energy representations of Diff (S1)
Projective unitary positive-energy representations of Diff (S1)
复制标题
Diff (S1) 的射影酉正能量表示
DOI：
10.1016/0022-1236(85)90090-4
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发表时间：
1985
影响因子：
1.7
通讯作者：
N. Wallach
中科院分区：
文献类型：
--
作者：
R. Goodman;N. Wallach
令 D 为圆 S 1 的保向微分同胚群。则 D 为 Fréchet 李群，李代数 (δ∞) R 为 S 1 上的光滑实向量场。令 δ R 为具有有限傅里叶级数的实向量场的子代数。证明了δ R 的每一个无限小酉射影正能量表示都可以积分成D 的连续射影酉表示。这个结果是由V. Kac 猜想的。
Let D be the group of orientation-preserving diffeomorphisms of the circle S 1. Then D is Fréchet Lie group with Lie algebra (δ∞) R the smooth real vector fields on S 1. Let δ R be the subalgebra of real vector fields with finite Fourier series. It is proved that every infinitesimally unitary projective positive-energy representation of δ R integrates to a continuous projective unitary representation of D. This result was conjectured by V. Kac.