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Lie Bialgebra Structures on the Centerless W-Algebra W(2,2)

Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China

Department of Mathematics, University of Science and Technology of China, Hefei 230026, China

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Department of Mathematics, University of Science and Technology of China, Hefei 230026, China

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Collage of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China

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https://doi.org/10.1142/S1005386710000192Cited by:17 (Source: Crossref)

Abstract

Verma modules over the W-algebra W(2,2) were considered by Zhang and Dong, while the Harish-Chandra modules and irreducible weight modules over this algebra were classified by Liu and Zhu etc. In the present paper, we investigate the Lie bialgebra structures on the centerless W-algebra, which are shown to be triangular coboundary.

Supported by the NSF (grants 10825101, 10861004, 10901028, 10926166) of China, the China Postdoctoral Science Foundation (grant 20080440720) and the Natural Science Research Projects of Jiangsu Education Committee (grants 08KJD110001, 09KJB110001).

Keywords:

AMSC: 17B05, 17B37, 17B62, 17B68

References

V. G. Drinfeld, Soviet Math. Dokl. 28(3), 667 (1983). Google Scholar
V. G. Drinfeld, Quantum groups, Proceeding of the International Congress of Mathematicians (Amer. Math. Soc., Providence, RI, 1987) pp. 798–820. Google Scholar
C. Grunspan, J. Algebra 280, 145 (2004), DOI: 10.1016/j.jalgebra.2004.04.016. Crossref, Web of Science, Google Scholar
J. Li, Y. Su and B. Xin, Chinese Annals of Math. (Series B) 29(5), 487 (2008), DOI: 10.1007/s11401-007-0447-x. Crossref, Web of Science, Google Scholar
D. Liu, S. Gao and L. Zhu, J. Math. Phys. 49, 113503 (2008), DOI: 10.1063/1.2996291. Crossref, Web of Science, Google Scholar
D. Liu, L. Zhu, Classification of Harish-Chandra modules over the W-algebra W(2, 2) , arXiv:0801.2601v2 . Google Scholar
W. Michaelis, Adv. Math. 38, 1 (1980), DOI: 10.1016/0001-8708(80)90056-0. Crossref, Web of Science, Google Scholar
W. Michaelis, Adv. Math. 57, 93 (1985), DOI: 10.1016/0001-8708(85)90051-9. Crossref, Web of Science, Google Scholar
W. Michaelis, Adv. Math. 107, 365 (1994), DOI: 10.1006/aima.1994.1062. Crossref, Web of Science, Google Scholar
S. H. Ng and E. J. Taft, J. Pure Appl. Algebra 151, 67 (2000), DOI: 10.1016/S0022-4049(99)00045-6. Crossref, Web of Science, Google Scholar
W. D. Nichols, J. Pure Appl. Algebra 68, 395 (1990), DOI: 10.1016/0022-4049(90)90091-U. Web of Science, Google Scholar
G. Song and Y. Su, Science in China (Series A) 49(4), 533 (2006), DOI: 10.1007/s11425-006-0533-7. Crossref, Web of Science, Google Scholar
E. J. Taft, J. Pure Appl. Algebra 87, 301 (1993), DOI: 10.1016/0022-4049(93)90116-B. Crossref, Web of Science, Google Scholar
Y. Wu, G. Song and Y. Su, Acta Mathematica Sinica (English Series) 22, 1915 (2006), DOI: 10.1007/s10114-005-0742-y. Crossref, Web of Science, Google Scholar
W. Zhang and C. Dong, Commun. Math. Phys. 285, 991 (2009), DOI: 10.1007/s00220-008-0562-x. Crossref, Web of Science, Google Scholar

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Vol. 17, No. 02

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History

Received 11 February 2008

Revised 4 August 2008

Keywords