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

^*Corresponding author for this work

School of Mathematical Sciences

York University Toronto

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

51 Scopus citations

Abstract

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 ), 〈 | 〉 ).

Original language	English
Pages (from-to)	378-405
Number of pages	28
Journal	Journal of Algebra
Volume	301
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2005.08.030
State	Published - 1 Jul 2006

Keywords

2-parameter quantum group
Drinfel'd double
Hopf (skew-)dual pairing
Lusztig's symmetry

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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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Y1 - 2006/7/1

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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DO - 10.1016/j.jalgebra.2005.08.030

M3 - 文章

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JO - Journal of Algebra

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ER -

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

Abstract

Keywords

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