KFU. Card publication. Flatness of Noetherian Hopf algebras over coideal subalgebras

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FLATNESS OF NOETHERIAN HOPF ALGEBRAS OVER COIDEAL SUBALGEBRAS

Form of presentation

Articles in international journals and collections

Year of publication

2020

Язык

английский

Authors, employees of KFU

Skryabin Sergey Markovich, author

Bibliographic description in the original language

Skryabin S., Flatness of Noetherian Hopf algebras over coideal subalgebras// Algebras and Representation Theory. - 2021. - Vol. 24, Is. 4, P. 851-875.

Annotation

It is proved in the paper that a Noetherian residually finite-dimensional Hopf algebra $H$ is a flat module over any right Noetherian right coideal subalgebra $A$. In the case when $A$ is a Hopf subalgebra we get faithful flatness. These results are obtained by verifying the existence of classical quotient rings of $A$ and $H$. It is also proved that the antipode of either right or left Noetherian residually finite-dimensional Hopf algebra is bijective. As a consequence, such a Hopf algebra is right and left Noetherian simultaneously.

Keywords

Hopf algebras, coideal subalgebras, flatness

The name of the journal

Algebras and Representation Theory

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85088533965&doi=10.1007%2fs10468-020-09972-y&partnerID=40&md5=68068b57bd1d7f2f05209d5f9bf7e88a

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=244768&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Skryabin Sergey Markovich	ru_RU
dc.date.accessioned	2020-01-01T00:00:00Z	ru_RU
dc.date.available	2020-01-01T00:00:00Z	ru_RU
dc.date.issued	2020	ru_RU
dc.identifier.citation	Skryabin S., Flatness of Noetherian Hopf algebras over coideal subalgebras// Algebras and Representation Theory. - 2021. - Vol. 24, Is. 4, P. 851-875.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=244768&p_lang=2	ru_RU
dc.description.abstract	Algebras and Representation Theory	ru_RU
dc.description.abstract	It is proved in the paper that a Noetherian residually finite-dimensional Hopf algebra $H$ is a flat module over any right Noetherian right coideal subalgebra $A$. In the case when $A$ is a Hopf subalgebra we get faithful flatness. These results are obtained by verifying the existence of classical quotient rings of $A$ and $H$. It is also proved that the antipode of either right or left Noetherian residually finite-dimensional Hopf algebra is bijective. As a consequence, such a Hopf algebra is right and left Noetherian simultaneously.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hopf algebras	ru_RU
dc.subject	coideal subalgebras	ru_RU
dc.subject	flatness	ru_RU
dc.title	Flatness of Noetherian Hopf algebras over coideal subalgebras	ru_RU
dc.type	Articles in international journals and collections	ru_RU