modular automorphism造句

The modular automorphism group of a von Neumann algebra " M " depends on the choice of state ?.
Connes discovered that changing the state does not change the image of the modular automorphism in the outer automorphism group of " M ".
Instead of being characterised by the simple affiliation relation " UAU " * = " A ", there is a more complicated bimodule relation involving the analytic continuation of the modular automorphism group.
It's difficult to find modular automorphism in a sentence. 用modular automorphism造句挺难的