On Lie Group-Lie Algebra Correspondences of Unitary Groups in Finite Von Neumann Algebras
On Lie Group-Lie Algebra Correspondences of Unitary Groups in Finite Von Neumann Algebras
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论李群-有限冯诺依曼代数中酉群的李代数对应
DOI：
10.1142/9789814343763_0003
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Yasumichi Matsuzawa
中科院分区：
文献类型：
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作者：
Hiroshi Ando;Yasumichi Matsuzawa
给出了在具有强算子拓扑的Hilbert空间$\mathcal {H}$中，酉群$U（\mathcal {H}）$的适当闭子群是否存在李代数的肯定答案.更精确地说，对于有限von Neumann代数$\mathfrak {M}$中酉群$U（\mathfrak {M}）$的任何强闭子群$G$，我们证明了$G$的强连续单参数子群的所有生成元的集合关于强预解式拓扑构成完备拓扑李代数.我们还刻画了代数$\mathfrak{M}$的所有密集定义的封闭运营商隶属于$\mathfrak{M}$从张量范畴的观点。
We give an affirmative answer to the question whether there exist Lie algebras for suitable closed subgroups of the unitary group $U(\mathcal{H})$ in a Hilbert space $\mathcal{H}$ with $U(\mathcal{H})$ equipped with the strong operator topology. More precisely, for any strongly closed subgroup $G$ of the unitary group $U(\mathfrak{M})$ in a finite von Neumann algebra $\mathfrak{M}$, we show that the set of all generators of strongly continuous one-parameter subgroups of $G$ forms a complete topological Lie algebra with respect to the strong resolvent topology. We also characterize the algebra $\mathfrak{M}$ of all densely defined closed operators affiliated with $\mathfrak{M}$ from the viewpoint of a tensor category.
DOI：
10.1007/978-1-4612-9839-7
发表时间：
1971
期刊：
--
影响因子：
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作者：
S. Lane
通讯作者：
S. Lane