Factor representations of diffeomorphism groups

Robert P. Boyer¹

¹ Department of Mathematics Drexel University Philadelphia, PA 19104, U.S.A.

Studia Mathematica, Tome 156 (2003) no. 2, pp. 105-120

Résumé

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.

Détail

DOI : 10.4064/sm156-2-2

Keywords: construction semifinite factor representations diffeomorphism group euclidean space these representations canonical correspondence finite factor representations inductive limit unitary group hence many these representations given terms quasi free representations canonical commutation anti commutation relations establish correspondence requires generalization complete positivity developed operator algebras compare asymptotic character formula unitary group thermodynamic limit construction diffeomorphism group representations