Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivska Street, 01601 Kyiv-4, UKRAINE
e-mail: vo@imath.kiev.ua
http://www.imath.kiev.ua/~vo/
 

On centered one-parameter semigroups and representations of double commutator

Abstract:
In this talk, we extend the notion of centered operator introduced by Morrel and Muhly to the continuous case of one-parameter semigroup. We study properties of such semigroups, in particular, we obtain description of one-parameter semigroups of partial isometries. Also, it is shown that there is natural correspondence between centered semigroups of operators  and representations of relation [a,[a,b]=0 by unbounded operators, similar to the correspondence between repesentations of Lie groups and Lie algebras.