T-property and nonisomorphic full factors of types II and III

AbstractThe actions of T-groups on von Neumann's hyperfinite algebras are studied. It is proved that there exist factors of type II with different countable fundamental groups and hence, different actions. It is also proved that there exist nonisomorphic full factors of type III1 with any fixed invariant Sd

Multi-operator colligations and multivariate characteristic functions

In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We construct characteristic functions for such double cosets and get semigroups of matrix-valued functions in matrix balls.Comment: 15p

Infinite tri-symmetric group, multiplication of double cosets, and checker topological field theories

We consider a product of three copies of infinite symmetric group and its representations spherical with respect to the diagonal subgroup. We show that such representations generate functors from a certain category of simplicial two-dimensional surfaces to the category of Hilbert spaces and bounded linear operators.Comment: 29 pages, 10 figure