Crystal Algebra

Jintai Ding

doi:10.1007/BF00398318

Crystal Algebra

Jintai Ding^*

^*Corresponding author for this work

Kyoto University

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

Abstract

We define the crystal algebra, an algebra which has a base of elements of crystal bases of a quantum group. The multiplication is defined by the tensor product rule of crystal bases. A universal n-colored crystal algebra is defined. We study the relation between those algebras and the tensor algebras of the crystal algebra of U_q(sl(2)) and give a presentation by generators and relations for the case of U_q(sl(n)).

Original language	English
Pages (from-to)	177-183
Number of pages	7
Journal	Letters in Mathematical Physics
Volume	38
Issue number	2
DOIs	https://doi.org/10.1007/BF00398318
Publication status	Published - 1996
Externally published	Yes

Keywords

Crystal algebra
Quantum group

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10.1007/BF00398318

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title = "Crystal Algebra",

abstract = "We define the crystal algebra, an algebra which has a base of elements of crystal bases of a quantum group. The multiplication is defined by the tensor product rule of crystal bases. A universal n-colored crystal algebra is defined. We study the relation between those algebras and the tensor algebras of the crystal algebra of Uq(sl(2)) and give a presentation by generators and relations for the case of Uq(sl(n)).",

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author = "Jintai Ding",

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journal = "Letters in Mathematical Physics",

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AU - Ding, Jintai

PY - 1996

Y1 - 1996

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AB - We define the crystal algebra, an algebra which has a base of elements of crystal bases of a quantum group. The multiplication is defined by the tensor product rule of crystal bases. A universal n-colored crystal algebra is defined. We study the relation between those algebras and the tensor algebras of the crystal algebra of Uq(sl(2)) and give a presentation by generators and relations for the case of Uq(sl(n)).

KW - Crystal algebra

KW - Quantum group

UR - https://www.scopus.com/pages/publications/1542638706

U2 - 10.1007/BF00398318

DO - 10.1007/BF00398318

M3 - Article

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SN - 0377-9017

VL - 38

SP - 177

EP - 183

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 2

ER -

Crystal Algebra

Abstract

Keywords

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