КФУ. Карточка публикации. On the graded algebras associated with Hecke symmetries

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ON THE GRADED ALGEBRAS ASSOCIATED WITH HECKE SYMMETRIES

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 Serge, On the graded algebras associated with Hecke symmetries//JOURNAL OF NONCOMMUTATIVE GEOMETRY. - 2020. - Vol.14, Is.3. - P.937-986.

Аннотация

A Hecke symmetry $R$ on a finite dimensional vector space $V$ gives rise to two graded factor algebras $\bbS(V,R)$ and $\La(V,R)$ of the tensor algebra of $V$ which are regarded as quantum analogs of the symmetric and the exterior algebras. Another graded algebra associated with $R$ is the Faddeev-Reshetikhin-Takhtajan bialgebra $A(R)$ which coacts on $\bbS(V,R)$ and $\La(V,R)$. There are also more general graded algebras defined with respect to pairs of Hecke symmetries and interpreted in terms of quantum hom-spaces. Their nice behaviour has been known under the assumption that the parameter $q$ of the Hecke relation is such that $1+q+\ldots+q^{n-1}\ne0$ for all $n>0$. The present paper makes an attempt to investigate several questions without this condition on $q$. Particularly we are interested in Koszulness and Gorensteinness of those graded algebras. For $q$ a root of 1 positive results require a restriction on the indecomposable modules for the Hecke algebras of type $A$ that can occur as direct summands of epresentations in the tensor powers of $V$.

Ключевые слова

Hecke symmetries, graded algebras, Koszul algebras, Gorenstein algebras, quantum symmetric algebras, FRT bialgebras, quantum hom-spaces, quantum groups

Название журнала

JOURNAL OF NONCOMMUTATIVE GEOMETRY

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https://repository.kpfu.ru/?p_id=244769

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 Serge, On the graded algebras associated with Hecke symmetries//JOURNAL OF NONCOMMUTATIVE GEOMETRY. - 2020. - Vol.14, Is.3. - P.937-986.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=244769	ru_RU
dc.description.abstract	JOURNAL OF NONCOMMUTATIVE GEOMETRY	ru_RU
dc.description.abstract	A Hecke symmetry $R$ on a finite dimensional vector space $V$ gives rise to two graded factor algebras $\bbS(V,R)$ and $\La(V,R)$ of the tensor algebra of $V$ which are regarded as quantum analogs of the symmetric and the exterior algebras. Another graded algebra associated with $R$ is the Faddeev-Reshetikhin-Takhtajan bialgebra $A(R)$ which coacts on $\bbS(V,R)$ and $\La(V,R)$. There are also more general graded algebras defined with respect to pairs of Hecke symmetries and interpreted in terms of quantum hom-spaces. Their nice behaviour has been known under the assumption that the parameter $q$ of the Hecke relation is such that $1+q+\ldots+q^{n-1}\ne0$ for all $n>0$. The present paper makes an attempt to investigate several questions without this condition on $q$. Particularly we are interested in Koszulness and Gorensteinness of those graded algebras. For $q$ a root of 1 positive results require a restriction on the indecomposable modules for the Hecke algebras of type $A$ that can occur as direct summands of epresentations in the tensor powers of $V$.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hecke symmetries	ru_RU
dc.subject	graded algebras	ru_RU
dc.subject	Koszul algebras	ru_RU
dc.subject	Gorenstein algebras	ru_RU
dc.subject	quantum symmetric algebras	ru_RU
dc.subject	FRT bialgebras	ru_RU
dc.subject	quantum hom-spaces	ru_RU
dc.subject	quantum groups	ru_RU
dc.title	On the graded algebras associated with Hecke symmetries	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU