矩阵代数中Kadison-Singer格的分类

任院红, 陈改娟, 刘倩, 王宁

数学学报 ›› 2012, Vol. 55 ›› Issue (6) : 1145-1152.

PDF(422 KB)
PDF(422 KB)
数学学报 ›› 2012, Vol. 55 ›› Issue (6) : 1145-1152. DOI: 10.12386/A2012sxxb0110
论文

矩阵代数中Kadison-Singer格的分类

    任院红, 陈改娟, 刘倩, 王宁
作者信息 +

Classification of Kadison-Singer Lattices in Matrix Algebras

    Yuan Hong REN, Gai Juan CHEN, Qian LIU, Ning WANG
Author information +
文章历史 +

摘要

通过研究3阶矩阵代数M3(C)中不变子空间格L生成的vonNeumann代数L″,在相似意义下刻画了M3(C)中的所有Kadison-Singer格L,并将这些KS格完全分了类.

Abstract

In this paper, by discussing the von Neumann algebras L″ generated by the invariant subspace lattices L in M3(C), the authors have classified all Kadison- Singer lattices in the 3-order matrix algebra with respect to similarity.

关键词

Kadison-Singer格 / 投影 / 矩阵代数 / von Neumann代数

Key words

Kadison-Singer lattice / projection / matrix algebra / von Neumann algebra

引用本文

导出引用
任院红, 陈改娟, 刘倩, 王宁. 矩阵代数中Kadison-Singer格的分类. 数学学报, 2012, 55(6): 1145-1152 https://doi.org/10.12386/A2012sxxb0110
Yuan Hong REN, Gai Juan CHEN, Qian LIU, Ning WANG. Classification of Kadison-Singer Lattices in Matrix Algebras. Acta Mathematica Sinica, Chinese Series, 2012, 55(6): 1145-1152 https://doi.org/10.12386/A2012sxxb0110

参考文献

[1] Ge L., Yuan W., Kadison-Singer algebras, I: hyperfinite case, Proc. Natl. Acad. USA, 2010, 107(5): 1838-1843.
[2] Ge L., Yuan W., Kadison-Singer algebras, II: General case, Proc. Natl. Acad. USA, 2010, 107(11): 4840-4844.
[3] Davidson K. R., Nest Algebras, Pitman Research Notes in Mathematics Series, Vol. 191, Longman Scientific& Technical, New York, 1988.
[4] Ringrose J., On some algebral of operators, II, Proc. London Math. Soc., 1966, 16(3): 385-402.
[5] Hou C. J., Cohomology of a class of Kadison-Singer algebras, Science in China Series, A: Mathematics,2010, 53: 1827-1839.
[6] Dong A. J., Hou C. J., Tan J., Classification of Kadison-Singer lattices in matrix algebras, Acta MathematicaSinica, Chinese Series, 2011, 54(2): 333-342.

基金

天元基金(11126349), 重庆市科委基金(2010BB9318)和重庆师范大学基金(10XLZ001)部分资助
PDF(422 KB)

Accesses

Citation

Detail

段落导航
相关文章

/