Drinfel'd doubles and Lusztig's symmetries of two-parameter quantum groups

Nantel Bergeron; Yun Gao; Naihong Hu

doi:10.1016/j.jalgebra.2005.08.030

Drinfel'd doubles and Lusztig's symmetries of two-parameter quantum groups

Nantel Bergeron^*
, Yun Gao
, Naihong Hu

^*此作品的通讯作者

数学科学学院

York University Toronto

科研成果: 期刊稿件 › 文章 › 同行评审

53 引用（Scopus）

摘要

We find the defining structures of two-parameter quantum groups U_r,s ( g ) corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd doubles. We further investigate the environment conditions upon which the Lusztig's symmetries exist between ( U_{r, s} ( g ), 〈, 〉 ) and its associated object ( U_s^-1, r^-1 ( g ), 〈 | 〉 ).

源语言	英语
页（从-至）	378-405
页数	28
期刊	Journal of Algebra
卷	301
期	1
DOI	https://doi.org/10.1016/j.jalgebra.2005.08.030
出版状态	已出版 - 1 7月 2006

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abstract = "We find the defining structures of two-parameter quantum groups Ur,s ( g ) corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd doubles. We further investigate the environment conditions upon which the Lusztig's symmetries exist between ( Ur, s ( g ), 〈, 〉 ) and its associated object ( Us-1, r-1 ( g ), 〈 | 〉 ).",

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N2 - We find the defining structures of two-parameter quantum groups Ur,s ( g ) corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd doubles. We further investigate the environment conditions upon which the Lusztig's symmetries exist between ( Ur, s ( g ), 〈, 〉 ) and its associated object ( Us-1, r-1 ( g ), 〈 | 〉 ).

AB - We find the defining structures of two-parameter quantum groups Ur,s ( g ) corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd doubles. We further investigate the environment conditions upon which the Lusztig's symmetries exist between ( Ur, s ( g ), 〈, 〉 ) and its associated object ( Us-1, r-1 ( g ), 〈 | 〉 ).

KW - 2-parameter quantum group

KW - Drinfel'd double

KW - Hopf (skew-)dual pairing

KW - Lusztig's symmetry

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Drinfel'd doubles and Lusztig's symmetries of two-parameter quantum groups

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