Another admissible quantum affine algebra of type A1(1) with quantum Weyl group

Ge Feng; Naihong Hu; Rushu Zhuang

doi:10.1016/j.geomphys.2021.104218

Another admissible quantum affine algebra of type A₁⁽¹⁾ with quantum Weyl group

Ge Feng, Naihong Hu, Rushu Zhuang

School of Mathematical Sciences

East China Normal University

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

3 Scopus citations

Abstract

The article is a continuation of Hu and Zhuang (2021), we construct another admissible quantum affine algebra U_q(sl̂₂) of affine type A₁⁽¹⁾ with different defining structural constants and variant q-Serre relations, its present formulae of the quantum root vectors are more involved than those in Hu and Zhuang (2021). We prove that as Hopf algebras, U_q(sl̂₂) is neither isomorphic to the standard quantum affine algebra U_q(sl̂₂) nor to the one U_q(sl̂₂) constructed in Hu and Zhuang (2021). The new quantum affine algebra has also the quantum Weyl group as its automorphism subgroup, by which its quantum root vectors are well-characterized, and leads to a description of the Poincaré-Birkhoff–Witt basis in terms of the Chevalley generators.

Original language	English
Article number	104218
Journal	Journal of Geometry and Physics
Volume	165
DOIs	https://doi.org/10.1016/j.geomphys.2021.104218
State	Published - Jul 2021

Keywords

New admissible quantum affine algebra U(sl̂)
PBW basis
Quantum Weyl group

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10.1016/j.geomphys.2021.104218

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title = "Another admissible quantum affine algebra of type A1(1) with quantum Weyl group",

abstract = "The article is a continuation of Hu and Zhuang (2021), we construct another admissible quantum affine algebra Uq(s{\^l}2) of affine type A1(1) with different defining structural constants and variant q-Serre relations, its present formulae of the quantum root vectors are more involved than those in Hu and Zhuang (2021). We prove that as Hopf algebras, Uq(s{\^l}2) is neither isomorphic to the standard quantum affine algebra Uq(s{\^l}2) nor to the one Uq(s{\^l}2) constructed in Hu and Zhuang (2021). The new quantum affine algebra has also the quantum Weyl group as its automorphism subgroup, by which its quantum root vectors are well-characterized, and leads to a description of the Poincar{\'e}-Birkhoff–Witt basis in terms of the Chevalley generators.",

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T1 - Another admissible quantum affine algebra of type A1(1) with quantum Weyl group

AU - Feng, Ge

AU - Hu, Naihong

AU - Zhuang, Rushu

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AB - The article is a continuation of Hu and Zhuang (2021), we construct another admissible quantum affine algebra Uq(sl̂2) of affine type A1(1) with different defining structural constants and variant q-Serre relations, its present formulae of the quantum root vectors are more involved than those in Hu and Zhuang (2021). We prove that as Hopf algebras, Uq(sl̂2) is neither isomorphic to the standard quantum affine algebra Uq(sl̂2) nor to the one Uq(sl̂2) constructed in Hu and Zhuang (2021). The new quantum affine algebra has also the quantum Weyl group as its automorphism subgroup, by which its quantum root vectors are well-characterized, and leads to a description of the Poincaré-Birkhoff–Witt basis in terms of the Chevalley generators.

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DO - 10.1016/j.geomphys.2021.104218

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Another admissible quantum affine algebra of type A₁⁽¹⁾ with quantum Weyl group

Abstract

Keywords

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