KFU. Card publication. On the graded algebras associated with Hecke symmetries, II. The Hilbert series

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ON THE GRADED ALGEBRAS ASSOCIATED WITH HECKE SYMMETRIES, II. THE HILBERT SERIES

Form of presentation

Articles in international journals and collections

Year of publication

2022

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Authors, employees of KFU

Skryabin Sergey Markovich, author

Bibliographic description in the original language

Skryabin Serge, On the graded algebras associated with Hecke symmetries, II. The Hilbert series//JOURNAL OF ALGEBRAIC COMBINATORICS. - 2022. - Vol. 56, P. 169-214.

Annotation

Hecke symmetries give rise to a family of graded algebras which represent quantum groups and spaces of noncommutative geometry. The present paper continues the work aiming to understand general properties of these algebras without a restriction on the parameter $q$ of Hecke relation used in earlier results. However, if $q$ is a root of 1, we need a restriction on the indecomposable modules for the Hecke algebras of type $A$ that can occur as direct summands of representations in the tensor powers of the initial vector space $V$. In this setting we generalize known results on rationality of Hilbert series. The combinatorial nature of this problem stems from a relationship between the Grothendieck ring of the category of comodules for the Faddeev-Reshetikhin-Takhtajan bialgebra $A(R)$ associated with a Hecke symmetry $R$ and the ring of symmetric functions. We then improve two results on monoidal equivalences of corepresentation categories and on Gorensteinness of graded algebras from a previous article.

Keywords

Hecke symmetries, graded algebras, Hilbert series

The name of the journal

JOURNAL OF ALGEBRAIC COMBINATORICS

URL

https://rdcu.be/cFbQF

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

https://repository.kpfu.ru/eng/?p_id=264024&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Skryabin Sergey Markovich	ru_RU
dc.date.accessioned	2022-01-01T00:00:00Z	ru_RU
dc.date.available	2022-01-01T00:00:00Z	ru_RU
dc.date.issued	2022	ru_RU
dc.identifier.citation	Skryabin Serge, On the graded algebras associated with Hecke symmetries, II. The Hilbert series//JOURNAL OF ALGEBRAIC COMBINATORICS. - 2022. - Vol. 56, P. 169-214.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=264024&p_lang=2	ru_RU
dc.description.abstract	JOURNAL OF ALGEBRAIC COMBINATORICS	ru_RU
dc.description.abstract	Hecke symmetries give rise to a family of graded algebras which represent quantum groups and spaces of noncommutative geometry. The present paper continues the work aiming to understand general properties of these algebras without a restriction on the parameter $q$ of Hecke relation used in earlier results. However, if $q$ is a root of 1, we need a restriction on the indecomposable modules for the Hecke algebras of type $A$ that can occur as direct summands of representations in the tensor powers of the initial vector space $V$. In this setting we generalize known results on rationality of Hilbert series. The combinatorial nature of this problem stems from a relationship between the Grothendieck ring of the category of comodules for the Faddeev-Reshetikhin-Takhtajan bialgebra $A(R)$ associated with a Hecke symmetry $R$ and the ring of symmetric functions. We then improve two results on monoidal equivalences of corepresentation categories and on Gorensteinness of graded algebras from a previous article.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hecke symmetries	ru_RU
dc.subject	graded algebras	ru_RU
dc.subject	Hilbert series	ru_RU
dc.title	On the graded algebras associated with Hecke symmetries, II. The Hilbert series	ru_RU
dc.type	Articles in international journals and collections	ru_RU