Two-parameter quantum affine algebra of type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:math>, Drinfeld realization and vertex representation

Hu, Naihong; Zhang, Honglian

doi:10.1016/j.jalgebra.2016.03.031

Cited by 6 publications

(2 citation statements)

References 29 publications

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“…More precisely, we set I to be the two-sided ideal generated by the elements K i − K ′−1 i , which is also a Z 2 -graded Hopf ideal, and we have canonical isomorphism D(U 0 , U 0 )/I ∼ = U q (g) as Z 2 -graded Hopf algebras. Recently, Drinfeld doubles have been studied by various authors as a useful tool to recover the quantum groups (see, e.g., [5,12,13,20,21,22]).…”

Section: Proposition 43mentioning

confidence: 99%

On the Harish-Chandra Homomorphism for Quantum Superalgebras

Luo,

Wang,

2021

Preprint

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In this paper, we introduce the Harish-Chandra homomorphism for the quantum superalgebra Uq(g) associated with a simple basic Lie superalgebra g and give an explicit description of its image. We use it to prove that the center of Uq(g) is isomorphic to a subring of the ring J(g) of exponential super-invariants in the sense of Sergeev and Veselov, establishing a Harish-Chandra type theorem for Uq(g). As a byproduct, we obtain a basis of the center of Uq(g) with the aid of quasi-R-matrix.

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Section: Proposition 43mentioning

confidence: 99%

On the Harish-Chandra Homomorphism for Quantum Superalgebras

Luo,

Wang,

2021

Preprint

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“…Hu, Rosso and Zhang [HRZ] first studied the Drinfeld realization of the two-parameter quantum affine algebra in type A by constructing its quantum Lyndon basis and the vertex representation. Furthermore, vertex representations of two-parameter quantum affine algebras in other types were also considered in [HZ1,HZ2,GHZ].…”

Section: Introductionmentioning

confidence: 99%