Monoidal categorification and quantum affine algebras

Masaki Kashiwara; Myungho Kim; Se Jin Oh; Euiyong Park

doi:10.1112/S0010437X20007137

Monoidal categorification and quantum affine algebras

Masaki Kashiwara
, Myungho Kim
, Se Jin Oh
, Euiyong Park

Kyoto University
Korea Institute for Advanced Study
Kyung Hee University
Ewha Womans University
University of Seoul

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

We introduce and investigate new invariants of pairs of modules M and N over quantum ane algebras U (g) by analyzing their associated R-matrices. Using these new invariants, we provide a criterion for a monoidal category of nite-dimensional integrable U0q (g)-modules to become a monoidal categori cation of a cluster algebra.

Original language	English
Pages (from-to)	1039-1077
Number of pages	39
Journal	Compositio Mathematica
DOIs	https://doi.org/10.1112/S0010437X20007137
State	Accepted/In press - 2020
Externally published	Yes

Keywords

13F60
17B37
18D10
2010 Mathematics Subject Classification

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10.1112/S0010437X20007137

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title = "Monoidal categorification and quantum affine algebras",

abstract = "We introduce and investigate new invariants of pairs of modules M and N over quantum ane algebras U (g) by analyzing their associated R-matrices. Using these new invariants, we provide a criterion for a monoidal category of nite-dimensional integrable U0q (g)-modules to become a monoidal categori cation of a cluster algebra.",

keywords = "13F60, 17B37, 18D10, 2010 Mathematics Subject Classification",

author = "Masaki Kashiwara and Myungho Kim and Oh, \{Se Jin\} and Euiyong Park",

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year = "2020",

doi = "10.1112/S0010437X20007137",

language = "English",

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journal = "Compositio Mathematica",

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AU - Kashiwara, Masaki

AU - Kim, Myungho

AU - Oh, Se Jin

AU - Park, Euiyong

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N2 - We introduce and investigate new invariants of pairs of modules M and N over quantum ane algebras U (g) by analyzing their associated R-matrices. Using these new invariants, we provide a criterion for a monoidal category of nite-dimensional integrable U0q (g)-modules to become a monoidal categori cation of a cluster algebra.

AB - We introduce and investigate new invariants of pairs of modules M and N over quantum ane algebras U (g) by analyzing their associated R-matrices. Using these new invariants, we provide a criterion for a monoidal category of nite-dimensional integrable U0q (g)-modules to become a monoidal categori cation of a cluster algebra.

KW - 13F60

KW - 17B37

KW - 18D10

KW - 2010 Mathematics Subject Classification

UR - https://www.scopus.com/pages/publications/85084401416

U2 - 10.1112/S0010437X20007137

DO - 10.1112/S0010437X20007137

M3 - Article

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SN - 0010-437X

SP - 1039

EP - 1077

JO - Compositio Mathematica

JF - Compositio Mathematica

ER -

Monoidal categorification and quantum affine algebras

Abstract

Keywords

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