Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 4: 707 - 730

DOI: https://doi.org/10.1007/s11464-011-0144-7

RESEARCH ARTICLE

Associating quantum vertex algebras to deformed Heisenberg Lie algebras

  • Haisheng LI
Expand
  • Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA

Received date: 11 Mar 2011

Accepted date: 19 May 2011

Published date: 01 Aug 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

We associate quantum vertex algebras and their ϕ-coordinated quasi modules to certain deformed Heisenberg algebras.

Key words： quantum vertex algebra; deformed Heisenberg Lie algebra; ϕ-coordinated module

Cite this article

Haisheng LI . Associating quantum vertex algebras to deformed Heisenberg Lie algebras[J]. Frontiers of Mathematics in China, 2011 , 6(4) : 707 -730 . DOI: 10.1007/s11464-011-0144-7

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Bouwknegt P, Pilch K. The deformed Virasoro algebra at roots of unity. Commun Math Phys, 1998, 196: 249-288

DOI

2
Etingof P, Frenkel I, Kirillov A Jr. Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations. Math Surveys and Monographs, Vol 58. Providence: AMS, 1998

3
Etingof P, Kazhdan D. Quantization of Lie bialgebras, V. Selecta Mathematica, New Series, 2000, 6: 105-130

4
Frenkel E, Reshetikhin N. Quantum affine algebras and deformations of the Virasoro and W -algebra. Commun Math Phys, 1996, 178: 237-264

DOI

5
Frenkel I B, Jing N-H. Vertex representations of quantum affine algebras. Proc Natl Acad Sci USA, 1988, 85: 9373-9377

DOI

6
Frenkel I B, Zhu Y. Vertex operator algebras associated to representations of affine and Virasoro algebras. Duke Math J, 1992, 66: 123-168

DOI

7
Golenishcheva-Kutuzova M, Kac V. Γ-conformal algebras. J Math Phys, 1998, 39: 2290-2305

DOI

8
Golenishcheva-Kutuzova M, Lebedev D. Vertex operator representation of some quantum tori Lie algebras. Commun Math Phys, 1992, 148: 403-416

DOI

9
Karel M, Li H-S. Some quantum vertex algebras of Zamolodchikov-Faddeev type. Commun Contemp Math, 2009, 11: 829-863

DOI

10
Lepowsky J, Li H-S. Introduction to Vertex Operator Algebras and Their Representations. Progress in Mathematics, Vol 227. Boston: Birkhäuser, 2003

11
Li H-S. Local systems of vertex operators, vertex superalgebras and modules. J Pure Appl Alg, 1996, 109: 143-195

DOI

12
Li H-S. Nonlocal vertex algebras generated by formal vertex operators. Selecta Mathematica, New Series, 2005, 11: 349-397

13
Li H-S. Constructing quantum vertex algebras. Int J Math, 2006, 17: 441-476

DOI

14
Li H-S. A new construction of vertex algebras and quasi modules for vertex algebras. Adv Math, 2006, 202: 232-286

DOI

15
Li H-S. Quantum vertex algebras and their ϕ-coordinated modules. arXiv: 0906.2710 [math.QA]

Options
Outlines

/

〈 〉