Idempotent States and the Inner Linearity Property

Teodor Banica; Uwe Franz; Adam Skalski

Bulletin of the Polish Academy of Sciences. Mathematics (2012)

  • Volume: 60, Issue: 2, page 123-132
  • ISSN: 0239-7269

Abstract

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We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A → Mₙ(ℂ) is a finite-dimensional representation of a Hopf C*-algebra, we prove that the idempotent state associated to its Hopf image A' must be the convolution Cesàro limit of the linear functional φ = tr ∘ π. We then discuss some consequences of this result, notably to inner linearity questions.

How to cite

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Teodor Banica, Uwe Franz, and Adam Skalski. "Idempotent States and the Inner Linearity Property." Bulletin of the Polish Academy of Sciences. Mathematics 60.2 (2012): 123-132. <http://eudml.org/doc/281178>.

@article{TeodorBanica2012,
abstract = {We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A → Mₙ(ℂ) is a finite-dimensional representation of a Hopf C*-algebra, we prove that the idempotent state associated to its Hopf image A' must be the convolution Cesàro limit of the linear functional φ = tr ∘ π. We then discuss some consequences of this result, notably to inner linearity questions.},
author = {Teodor Banica, Uwe Franz, Adam Skalski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {idempotent state; Hopf image; inner linearity},
language = {eng},
number = {2},
pages = {123-132},
title = {Idempotent States and the Inner Linearity Property},
url = {http://eudml.org/doc/281178},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Teodor Banica
AU - Uwe Franz
AU - Adam Skalski
TI - Idempotent States and the Inner Linearity Property
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 2
SP - 123
EP - 132
AB - We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A → Mₙ(ℂ) is a finite-dimensional representation of a Hopf C*-algebra, we prove that the idempotent state associated to its Hopf image A' must be the convolution Cesàro limit of the linear functional φ = tr ∘ π. We then discuss some consequences of this result, notably to inner linearity questions.
LA - eng
KW - idempotent state; Hopf image; inner linearity
UR - http://eudml.org/doc/281178
ER -

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