Published February 13, 2024 | Version v1
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A class of finite-by-cocommutative Hopf algebras

Creators

  • 1. University of Almería
  • 2. Universidad Nacional de Córdoba
  • 3. Consejo Nacional de Investigaciones Científicas y Técnicas

Description

We present a rich source of Hopf algebras starting from a cofinite central extension of a Noetherian Hopf algebra and a subgroup of the algebraic group of characters of the central Hopf subalgebra. The construction is transparent from a Tannakian perspective. We determine when the new Hopf algebras are co-Frobenius, or cosemisimple, or Noetherian, or regular, or have finite Gelfand-Kirillov dimension.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

نقدم مصدرًا غنيًا لجبر Hopf بدءًا من امتداد مركزي cofinite لجبر Noetherian Hopf ومجموعة فرعية من المجموعة الجبرية من أحرف الجبر الفرعي Hopf المركزي. البناء شفاف من منظور تاناكي. نحدد متى تكون جبر هوبف الجديد مشتركًا مع فروبينيوس، أو مشتركًا، أو نويثيريان، أو منتظمًا، أو له بعد Gelfand - Kirillov محدود.

Translated Description (French)

Nous présentons une riche source d'algèbres de Hopf à partir d'une extension centrale cofinie d'une algèbre de Hopf noethérienne et d'un sous-groupe du groupe algébrique de caractères de la sous-algèbre de Hopf centrale. La construction est transparente d'un point de vue tannakien. Nous déterminons quand les nouvelles algèbres de Hopf sont co-Frobenius, ou cosemisimple, ou Noetherian, ou régulières, ou ont une dimension finie de Gelfand-Kirillov.

Translated Description (Spanish)

Presentamos una rica fuente de álgebras Hopf a partir de una extensión central cofinita de un álgebra Hopf noetheriana y un subgrupo del grupo algebraico de caracteres de la subálgebra Hopf central. La construcción es transparente desde una perspectiva tannakiana. Determinamos cuándo las nuevas álgebras de Hopf son co-Frobenius, o cosemisimple, o noetheriana, o regular, o tienen una dimensión finita de Gelfand-Kirillov.

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Additional details

Additional titles

Translated title (Arabic)
فئة من جبر هوبف المحدود بالتبديل
Translated title (French)
Une classe d'algèbres de Hopf finies par commutatives
Translated title (Spanish)
Una clase de álgebras Hopf finitas por cocommutativas

Identifiers

Other
https://openalex.org/W4391786806
DOI
10.5802/art.5

Is supplement to
https://openalex.org/W4300242493 (Other)
https://openalex.org/W4237460455 (Other)
https://openalex.org/W4235640979 (Other)
https://openalex.org/W2965436902 (Other)
https://openalex.org/W2964000396 (Other)
https://openalex.org/W2963810136 (Other)
https://openalex.org/W2192213291 (Other)
https://openalex.org/W2169972388 (Other)
https://openalex.org/W2128350666 (Other)
https://openalex.org/W1483710569 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Argentina

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