Factor representations of diffeomorphism groups
Tom 156 / 2003
Studia Mathematica 156 (2003), 105-120 MSC: Primary 22E65; Secondary 46L99, 81R10. DOI: 10.4064/sm156-2-2
We give a new construction of semifinite factor representations of the diffeomorphism group of euclidean space. These representations are in canonical correspondence with the finite factor representations of the inductive limit unitary group. Hence, many of these representations are given in terms of quasi-free representations of the canonical commutation and anti-commutation relations. To establish this correspondence requires a generalization of complete positivity as developed in operator algebras. We also compare the asymptotic character formula for the unitary group with the thermodynamic ($N/V$) limit construction for diffeomorphism group representations.