КФУ. Карточка публикации. 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

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2022

Язык

английский

Авторы, сотрудники КФУ

Скрябин Сергей Маркович, автор

Библиографическое описание на языке оригинала

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

Аннотация

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.

Ключевые слова

Hecke symmetries, graded algebras, Hilbert series

Название журнала

JOURNAL OF ALGEBRAIC COMBINATORICS

URL

https://rdcu.be/cFbQF

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https://repository.kpfu.ru/?p_id=264024

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Скрябин Сергей Маркович	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/?p_id=264024	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	Статьи в зарубежных журналах и сборниках	ru_RU