Monadic forgetful functors and (non-)presentability for C⁎- and
W⁎-algebras

J 2023

Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras

CHIRVASITU, Alexandru a Joanna KO

Základní údaje

Originální název

Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras

Autoři

CHIRVASITU, Alexandru a Joanna KO

Vydání

Journal of Pure and Applied Algebra, Elsevier B.V. 2023, 0022-4049

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10100 1.1 Mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL, URL

Impakt faktor

Impact factor: 0.700

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/23:00130024

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

C∗-algebra; W∗-algebra; Locally presented; Locally generated; Monadic; Beck’s theorem; Tripleability; Enriched

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 21. 11. 2022 11:08, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

We prove that the forgetful functors from the categories of C⁎- and W⁎-algebras to Banach ⁎-algebras, Banach algebras or Banach spaces are all monadic, answering a question of J.Rosický, and that the categories of unital (commutative) C⁎-algebras are not locally-isometry ℵ0-generated either as plain or as metric-enriched categories, answering a question of I. Di Liberti and Rosický. We also prove a number of negative presentability results for the category of von Neumann algebras: not only is that category not locally presentable, but in fact its only presentable objects are the two algebras of dimension ≤1. For the same reason, for a locally compact abelian group G the category of G-graded von Neumann algebras is not locally presentable.

Citovat

CHIRVASITU, Alexandru a Joanna KO. Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras. Journal of Pure and Applied Algebra. Elsevier B.V., 2023, roč. 227, č. 3, s. 1-24. ISSN 0022-4049. Dostupné z: https://doi.org/10.1016/j.jpaa.2022.107209.

@article{2219879,
   author = {Chirvasitu, Alexandru and Ko, Joanna},
   article_number = {3},
   doi = {https://doi.org/10.1016/j.jpaa.2022.107209},
   keywords = {C∗-algebra; W∗-algebra; Locally presented; Locally generated; Monadic; Beck’s theorem; Tripleability; Enriched},
   language = {eng},
   issn = {0022-4049},
   journal = {Journal of Pure and Applied Algebra},
   title = {Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras},
   url = {https://arxiv.org/pdf/2203.12087.pdf},
   volume = {227},
   year = {2023}
}

TY  - JOUR
ID  - 2219879
AU  - Chirvasitu, Alexandru - Ko, Joanna
PY  - 2023
TI  - Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras
JF  - Journal of Pure and Applied Algebra
VL  - 227
IS  - 3
SP  - 1-24
EP  - 1-24
PB  - Elsevier B.V.
SN  - 00224049
KW  - C∗-algebra
KW  - W∗-algebra
KW  - Locally presented
KW  - Locally generated
KW  - Monadic
KW  - Beck’s theorem
KW  - Tripleability
KW  - Enriched
UR  - https://arxiv.org/pdf/2203.12087.pdf
N2  - We prove that the forgetful functors from the categories of C⁎- and W⁎-algebras to Banach ⁎-algebras, Banach algebras or Banach spaces are all monadic, answering a question of J.Rosický, and that the categories of unital (commutative) C⁎-algebras are not locally-isometry ℵ0-generated either as plain or as metric-enriched categories, answering a question of I. Di Liberti and Rosický. We also prove a number of negative presentability results for the category of von Neumann algebras: not only is that category not locally presentable, but in fact its only presentable objects are the two algebras of dimension ≤1. For the same reason, for a locally compact abelian group G the category of G-graded von Neumann algebras is not locally presentable.
ER  -

CHIRVASITU, Alexandru a Joanna KO. Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras. \textit{Journal of Pure and Applied Algebra}. Elsevier B.V., 2023, roč.~227, č.~3, s.~1-24. ISSN~0022-4049. Dostupné z: https://doi.org/10.1016/j.jpaa.2022.107209.

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