摘要
研究了矩阵代数M_n(C)的KS格,证明了每个生成M_3(C)的KS格都相似于(?)_0或I-(?)_0,其中(?)_0为M_3(C)的一个极大对角投影套和一个赋值全非零的秩1投影所生成的KS格,从而M_3(C)的对角平凡的KS代数都是4维的.同时,还给出了几个生成M_4(C)但非同构的KS格的例子.
We study Kadison-Singer lattices in the matrix algebra M_n(C),and prove that each Kadison-Singer lattice generating M_3(C) as an algebra is similar to L_0 or I-L_0,where L_0 is the KS lattice generated by a maximal nest of diagonal projections and a rank one projection matrix with nonzero entries in M_3(C),hence each Kadison-Singer algebra with trivial diagonal in M_3(C) has dimension 4.In addition,we give some examples of nonisomorphic Kadison-Singer lattices which generate M_4(C).
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2011年第2期333-342,共10页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金资助项目(10971117)
山东省自然科学基金(ZR2009AQ005)