Kadison–Singer algebras, II: General case
Kadison–Singer algebras, II: General case
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DOI：
10.1073/pnas.0914150107
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
L. Ge;Wei Yuan
中科院分区：
文献类型：
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作者：
L. Ge;Wei Yuan
引入一类新的算子代数Kadison-Singer（KS-）代数.这些高度非交换的非自伴代数推广了三角矩阵代数。它们由冯诺依曼代数中对应于KS-代数对角线的交换子的投影的某些极小生成格决定。它表明，这些格和它们的约化形式往往同胚的经典流形，如球。
A new class of operator algebras, Kadison–Singer (KS-) algebras, is introduced. These highly noncommutative, non self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. It is shown that these lattices and their reduced forms are often homeomorphic to classical manifolds such as the sphere.