Ⅱ_∞型因子中套子代数的模换位

Modular commutants of nest subalgebras in type Ⅱ∞ factors

讨论了Ⅱ∞型因子ＶｏｎＮｅｕｍａｎｎ代数中套子代数关于理想Ｉｃ的模换位，证明了具有无限原子和约化数不小于２的套所对应的套子代数关于Ｉｃ的模换位是｛ＣＩ｝＋Ｉｃ；同时得到由这类套子代数到Ｉｃ的任一导子都是内导子．

The commutants of nest subalgebras of type Ⅱ∞ factor Von Neumann algebras module the ideal Ic in these factors are discussed. It is proved that the commutant of the algebra of a nest with an infinite atom and the algebra of a nest of which reduced number is not less than two modules the ideal Ic is {CI}+Ic, and it is simultaneously shown that every derivation from this class nest subalgebras into Ic is inner.