KFU. Card publication. On the graded algebras associated with Hecke symmetries

KAZAN
FEDERAL UNIVERSITY

- RUS
- 中文
- ES

ON THE GRADED ALGEBRAS ASSOCIATED WITH HECKE SYMMETRIES

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

Annotation

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 $V$.

Keywords

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

The name of the journal

JOURNAL OF NONCOMMUTATIVE GEOMETRY

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

https://repository.kpfu.ru/eng/?p_id=244769&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 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/eng/?p_id=244769&p_lang=2	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	Articles in international journals and collections	ru_RU