Lie theoretic significance of the measure topologies associated with a finite trace
Lie theoretic significance of the measure topologies associated with a finite trace
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与有限迹线相关的测量拓扑的理论意义
DOI：
10.1515/forum.2010.13
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
D. Beltiţă
中科院分区：
文献类型：
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作者：
D. Beltiţă
摘要：设[j]是具有忠实正规有限迹的W*-代数，并考虑具有超弱拓扑的酉群U [j]。利用与上述迹相关的测度拓扑，我们证明了U -是K.H. Hofmann和S.A. Morris （J.群论8:118 - 133,2005）意义上的具有李代数的拓扑群。我们讨论了相应的指数映射，并发现在II1型因子的情况下，它不是局部内射的。
Abstract Let ℳ be a W*-algebra with a faithful normal finite trace and think of the unitary group Uℳ endowed with the ultraweak topology. By using the measure topology associated with the aforementioned trace, we prove that Uℳ is a topological group with Lie algebra in the sense of K.H. Hofmann and S.A. Morris (J. Group Theory 8: 115–133, 2005). We discuss the corresponding exponential map and find that it is never locally injective in the case of factors of type II1.