矩阵代数中一类新的Kadison-Singer格
New Kadison-Singer Lattices in Matrix Algebras

作者: 陈改娟 * , 任院红 :重庆师范大学数学学院; 王 宁 * , 刘 倩 :;

关键词: Kadison-Singer格矩阵代数Kadison-Singer代数von Neumann代数Kadison-Singer Lattice Matrix Algebra Kadison-Singer Algebra von Neumann Algebra

摘要: 本文在矩阵代数M2(C)和M3(C)中由一个极大套和由一个分离向量决定的秩1投影生成的Kadison-Singer格及Kadison-Singer代数的基础上,将该类投影分别嵌入到矩阵代数M4(C)与M6(C)中,构造出了生成M4(C)与M6(C)Kadison-Singer格并计算出了相应的Kadison-Singer代数。

Abstract: For given Kadison-Singer lattices in  matrix algebras  M2(C) and M3(C)  which is generated by a maximal nest and rank 1 operator determined by a separating vector, the paper constructs new Kadison-Singer lattices in M4(C) and  M6(C)which generate the full matrix algebras M4(C)  and  M6(C)respectively.

文章引用: 陈改娟 , 任院红 , 王 宁 , 刘 倩 (2012) 矩阵代数中一类新的Kadison-Singer格。 理论数学, 2, 131-137. doi: 10.12677/PM.2012.23021

参考文献

[1] L. Ge, W. Yuan. Kadison-Singer algebras, I: Hyperfinite case. Proceedings of the National Academy of Sciences USA, 2010, 107(5): 1838- 1843.

[2] L. Ge, W. Yuan. Kadison-Singer algebras, II: General case. Proceedings of the National Academy of Sciences USA, 2010, 107(11): 4840- 4844.

[3] C. J. Hou. Cohomology of a class of Kadison-Singer algebras. Science in China Series A: Mathematics, 2010, 53: 1827-1839.

[4] K. H. Kim, F. W. Roush. Reflexive lattices of subspace. Proceedings of the American Mathematical Society, 1980, 78(11): 17-18.

[5] 董瑷菊, 侯成军, 谭君. 矩阵代数的Kadison-Singer格的分类[J]. 数学学报(中文版), 2011, 54(2): 333-342.

[6] 鲁世杰, 陆芳言, 李鹏同等. 非自伴算子代数[M]. 北京: 科学出版社, 2004: 4-7.

[7] 胡长流, 宋振明. 格论基础[M]. 开封: 河南大学出版社, 1990: 74.

分享
Top