Quantum group structure associated to the quantum affine space

Naihong Hu

Quantum group structure associated to the quantum affine space

Naihong Hu

School of Mathematical Sciences

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

9 Scopus citations

Abstract

A braided monoidal category G_Λθ of Λ-graded associative algebras over a field k is established. The structural feature (including its PBW-basis) of the braided universal enveloping algebra U(L) of a θ-Lie algebra L is investigated as an object in G _Λ,θ, and a class of quantum groups arising from U(L) is presented. In addition, the quantized universal enveloping algebra of any abelian Lie algebra is given, which is a twisted quantum group associated to the quantum affine space k(A_q^n|0].

Original language	English
Pages (from-to)	483-492
Number of pages	10
Journal	Algebra Colloquium
Volume	11
Issue number	4
State	Published - Dec 2004

Keywords

Braided Hopf algebra
Braided monoidal category
Quantum affine space
θ-Lie algebra

Cite this

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abstract = "A braided monoidal category GΛθ of Λ-graded associative algebras over a field k is established. The structural feature (including its PBW-basis) of the braided universal enveloping algebra U(L) of a θ-Lie algebra L is investigated as an object in G Λ,θ, and a class of quantum groups arising from U(L) is presented. In addition, the quantized universal enveloping algebra of any abelian Lie algebra is given, which is a twisted quantum group associated to the quantum affine space k(Aqn|0].",

keywords = "Braided Hopf algebra, Braided monoidal category, Quantum affine space, θ-Lie algebra",

author = "Naihong Hu",

year = "2004",

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pages = "483--492",

journal = "Algebra Colloquium",

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N2 - A braided monoidal category GΛθ of Λ-graded associative algebras over a field k is established. The structural feature (including its PBW-basis) of the braided universal enveloping algebra U(L) of a θ-Lie algebra L is investigated as an object in G Λ,θ, and a class of quantum groups arising from U(L) is presented. In addition, the quantized universal enveloping algebra of any abelian Lie algebra is given, which is a twisted quantum group associated to the quantum affine space k(Aqn|0].

AB - A braided monoidal category GΛθ of Λ-graded associative algebras over a field k is established. The structural feature (including its PBW-basis) of the braided universal enveloping algebra U(L) of a θ-Lie algebra L is investigated as an object in G Λ,θ, and a class of quantum groups arising from U(L) is presented. In addition, the quantized universal enveloping algebra of any abelian Lie algebra is given, which is a twisted quantum group associated to the quantum affine space k(Aqn|0].

KW - Braided Hopf algebra

KW - Braided monoidal category

KW - Quantum affine space

KW - θ-Lie algebra

UR - https://www.scopus.com/pages/publications/28044471543

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SN - 1005-3867

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SP - 483

EP - 492

JO - Algebra Colloquium

JF - Algebra Colloquium

IS - 4

ER -

Quantum group structure associated to the quantum affine space

Abstract

Keywords

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