L K Hua Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, China.
Proc Natl Acad Sci U S A. 2010 Mar 16;107(11):4840-4. doi: 10.1073/pnas.0914150107. Epub 2010 Feb 25.
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.
引入了一类新的算子代数，即 Kadison-Singer（KS）-代数。这些高度非交换、非自伴的代数推广了三角矩阵代数。它们由 KS-代数的对角元伴随的 von Neumann 代数中的某些投影的极小生成格确定。结果表明，这些格及其约化形式通常同胚于经典流形，如球面。
