Factor representations of diffeomorphism groups

Robert P. Boyer. "Factor representations of diffeomorphism groups." Studia Mathematica 156.2 (2003): 105-120. <http://eudml.org/doc/285254>.

@article{RobertP2003,
abstract = {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.},
author = {Robert P. Boyer},
journal = {Studia Mathematica},
keywords = {semifinite factor representation; infinite-dimensional groups; diffeomorphisms},
language = {eng},
number = {2},
pages = {105-120},
title = {Factor representations of diffeomorphism groups},
url = {http://eudml.org/doc/285254},
volume = {156},
year = {2003},
}

TY - JOUR
AU - Robert P. Boyer
TI - Factor representations of diffeomorphism groups
JO - Studia Mathematica
PY - 2003
VL - 156
IS - 2
SP - 105
EP - 120
AB - 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.
LA - eng
KW - semifinite factor representation; infinite-dimensional groups; diffeomorphisms
UR - http://eudml.org/doc/285254
ER -