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Peer-reviewedCC BYAdvances in Mathematics

Selfless reduced free products and graph products of C⁎-algebras

  • Felipe Flores1
  • Mario Klisse2
  • Mícheál Ó Cobhthaigh
  • Matteo Pagliero3
  1. 1Department of Mathematics, University of Virginia, Kerchof Hall. 141 Cabell Dr, Charlottesville, VA, United States
  2. 2Department of Mathematics, Christian-Albrechts University Kiel, Heinrich-Hecht-Platz 6, Kiel, Germany
  3. 3Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, Odense, Denmark
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Abstract

Under mild assumptions, we show that reduced free products and reduced graph products of C ⁎ -algebras are completely selfless, without assuming the rapid decay property. In particular, our main theorems yield numerous new examples of simple, monotracial C ⁎ -algebras with strict comparison, stable rank one, and admitting a unique unital embedding of the Jiang–Su algebra Z up to approximate unitary equivalence, and of purely infinite C ⁎ -algebras in the traceless case.

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Cite

BibTeXRIS
BibTeX
@article{flores2026selfless,
  title = {{Selfless reduced free products and graph products of C⁎-algebras}},
  author = {Felipe Flores and Mario Klisse and Mícheál Ó Cobhthaigh and Matteo Pagliero},
  journal = {Advances in Mathematics},
  year = {2026},
  month = aug,
  doi = {10.1016/j.aim.2026.111190},
  url = {https://doi.org/10.1016/j.aim.2026.111190},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Selfless reduced free products and graph products of C⁎-algebras
AU  - Felipe Flores
AU  - Mario Klisse
AU  - Mícheál Ó Cobhthaigh
AU  - Matteo Pagliero
PY  - 2026
DA  - 2026/08/18
JO  - Advances in Mathematics
DO  - 10.1016/j.aim.2026.111190
UR  - https://doi.org/10.1016/j.aim.2026.111190
AB  - Under mild assumptions, we show that reduced free products and reduced graph products of C ⁎ -algebras are completely selfless, without assuming the rapid decay property. In particular, our main theorems yield numerous new examples of simple, monotracial C ⁎ -algebras with strict comparison, stable rank one, and admitting a unique unital embedding of the Jiang–Su algebra Z up to approximate unitary equivalence, and of purely infinite C ⁎ -algebras in the traceless case.
SN  - 0001-8708
SN  - 1090-2082
ER  -