TY - JOUR

T1 - Gauge groups of E0-semigroups obtained from powers weights

AU - Jankowski, Christopher

AU - Markiewicz, Daniel

N1 - Funding Information:
This work was partially supported by the Skirball Foundation via the Center for Advanced Studies in Mathematics at Ben-Gurion University of the Negev to C.J.; and this work was partially supported by a grant from the U.S.-Israel Binational Science Foundation to D.M.

PY - 2012/7/23

Y1 - 2012/7/23

N2 - The gauge group is computed explicitly for a family of E0-semigroups of type II0 arising from the boundary weight double construction introduced earlier by Jankowski. This family contains many E0-semigroups that are not cocycle conjugate to any examples whose gauge groups have been computed earlier. Further results are obtained regarding the classification up to cocycle conjugacy and up to conjugacy for boundary weight doubles (φ,ν) in two separate cases: first in the case when φ is unital, invertible and q-pure, and ν is any type II Powers weight, and secondly when φ is a unital q-positive map whose range has dimension one and ν(A)=(f,Af) for some function f such that. (1-e -x) 1/2 f)x) ∈ L 2 (0, ∞). All E 0-semigroups in the former case are cocycle conjugate to the one arising simply from ν, and any two E0-semigroups in the latter case are cocycle conjugate if and only if they are conjugate.

AB - The gauge group is computed explicitly for a family of E0-semigroups of type II0 arising from the boundary weight double construction introduced earlier by Jankowski. This family contains many E0-semigroups that are not cocycle conjugate to any examples whose gauge groups have been computed earlier. Further results are obtained regarding the classification up to cocycle conjugacy and up to conjugacy for boundary weight doubles (φ,ν) in two separate cases: first in the case when φ is unital, invertible and q-pure, and ν is any type II Powers weight, and secondly when φ is a unital q-positive map whose range has dimension one and ν(A)=(f,Af) for some function f such that. (1-e -x) 1/2 f)x) ∈ L 2 (0, ∞). All E 0-semigroups in the former case are cocycle conjugate to the one arising simply from ν, and any two E0-semigroups in the latter case are cocycle conjugate if and only if they are conjugate.

UR - http://www.scopus.com/inward/record.url?scp=84863896509&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnr142

DO - 10.1093/imrn/rnr142

M3 - Article

AN - SCOPUS:84863896509

SN - 1073-7928

VL - 2012

SP - 3278

EP - 3310

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 14

ER -