A twisted quantum toroidal algebra

Naihuan JING; Rong jia LIU

doi:10.1007/s11464-013-0316-8

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Front. Math. China ›› 2013, Vol. 8 ›› Issue (5) : 1117-1128. DOI: 10.1007/s11464-013-0316-8

RESEARCH ARTICLE

A twisted quantum toroidal algebra

Naihuan JING¹^,² ,
Rong jia LIU¹

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Abstract

As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra of type A₁ is introduced. Explicit realization of the new quantum TKK algebra is constructed with the help of twisted quantum vertex operators over a Fock space.

Keywords

Vertex operator / toroidal algebra / quantum algebra

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Naihuan JING, Rong jia LIU. A twisted quantum toroidal algebra. Front Math Chin, 2013, 8(5): 1117‒1128 https://doi.org/10.1007/s11464-013-0316-8

References

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[1]	Frenkel I B. Representation of Kac-Moody algebras and dual resonance models. In: Applications of Group Theory in Physics and Mathematical Physics (Chicago, 1982), Lect Appl Math. Providence: Amer Math Soc, 1985, 325-353

[2]	Frenkel I B, Jing N. Vertex representations of quantum affine algebras. Proc Natl Acad Sci USA, 1988, 85: 9373-9377 CrossRef Google scholar

[3]	Frenkel I B, Jing N, Wang W. Quantum vertex representations via finite groups and the Mckay correspondence. Comm Math Phys, 2000, 211: 365-393 CrossRef Google scholar

[4]	Gao Y, Jing N. Uq(l^N) action on l^N-modules and quantum toroidal algebras. J Algebra, 2004, 273: 320-343 CrossRef Google scholar

[5]	Gao Y, Jing N. A quantized Tits-Kantor-Koecher algebra. Algebr Represent Theory, 2010, 2: 207-217

[6]	Ginzburg V, Kapranov M, Vasserot E. Langlands reciprocity for algebraic surfaces. Math Res Lett, 1995, 2: 147-160

[7]	Jing N. Twisted vertex representations of quantum affine algebras. Invent Math, 1990, 102: 663-690 CrossRef Google scholar

[8]	Jing N. Quantum Kac-Moody algebras and vertex representations. Lett Math Phys, 1998, 44: 261-271 CrossRef Google scholar

[9]	Jing N. New twisted quantum current algebras. In: Wang J, Lin Z, eds. Representa-tions and Quantizations. Beijing: Higher Education Press and Springer, 2000

[10]	Chen F, Gao Y, Jing N, Tan S. Twisted vertex operators and unitary Lie algebras. 2011, preprint

[11]	Moody R V, Rao S E, Yokonuma T. Toroidal Lie algebras and vertex representations. Geom Dedicata, 1990, 35: 283-307 CrossRef Google scholar

[12]	Saito Y. Quantum toroidal algebras and their vertex representations. Publ RIMS Kyoto Univ, 1998, 34: 155-177 CrossRef Google scholar

[13]	Saito Y, Takemura K, Uglov D. Toroidal actions on level-1 modules of Uq(sl^N). Transform Groups, 1998, 3: 75-102 CrossRef Google scholar

[14]	Takemura K, Uglov D. Representations of the quantum toroidal algebra on highest weight modules of the quantum affine algebra of type lN. Publ RIMS Kyoto Univ, 1999, 35: 407-450 CrossRef Google scholar