DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS
DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS
复制标题
局部紧群上伪函数的直有限代数
DOI：
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发表时间：
2012
影响因子：
0.5
通讯作者：
Yemon Choi
中科院分区：
文献类型：
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作者：
Yemon Choi
一个代数A称为直有限的，如果A的（条件）单位化中的每个左可逆元都是右可逆的。我们证明了么模群的约化群C*-代数是直接有限的，推广了离散情形的已知结果。我们还研究了p-伪函数代数的相应问题，证明了这些代数是直接有限的，如果G是顺从的和幺模的，或幺模的Kunze-Stein性质。本文还讨论了当G是真实的或复直线的仿射群时，文献中已有的结果如何暗示L1（G）不是直接有限的.
Abstract An algebra A is said to be directly finite if each left-invertible element in the (conditional) unitization of A is right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras of p-pseudofunctions, showing that these algebras are directly finite if G is amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply that L1(G) is not directly finite when G is the affine group of either the real or complex line.