КФУ. Карточка публикации. Flatness of Noetherian Hopf algebras over coideal subalgebras

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FLATNESS OF NOETHERIAN HOPF ALGEBRAS OVER COIDEAL SUBALGEBRAS

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2020

Язык

английский

Авторы, сотрудники КФУ

Скрябин Сергей Маркович, автор

Библиографическое описание на языке оригинала

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

Аннотация

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.

Ключевые слова

Hopf algebras, coideal subalgebras, flatness

Название журнала

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

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https://repository.kpfu.ru/?p_id=244768

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Скрябин Сергей Маркович	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/?p_id=244768	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	Статьи в зарубежных журналах и сборниках	ru_RU