Acta mathematica scientia, Series B >
QUANTIZATION OF LIE ALGEBRAS OF BLOCK TYPE
Received date: 2007-04-23
Revised date: 2008-07-15
Online published: 2010-07-20
Supported by
Project supported by the National Science Foundation of China (10825101), "One Hundred Talents Program'' from University of Science and Technology of China, and the China Postdoctoral Science Foundation (20090450810)
In this article, we use the general method of quantization by Drinfeld's twist to quantize explicitly the Lie bialgebra structures on Lie algebras of Block type.
Key words: Quantization; Lie bialgebras; Drinfeld twist; Lie algebras of Block type
CHENG Yong-Sheng , SU Yu-Cai . QUANTIZATION OF LIE ALGEBRAS OF BLOCK TYPE[J]. Acta mathematica scientia, Series B, 2010 , 30(4) : 1134 -1142 . DOI: 10.1016/S0252-9602(10)60111-7
[1] Cheng Y, Song G, Xin B. Lie bialgebra structures on Lie algebras of Block type. Algebra Colloq, 2009, 16(4): 677--690
[2] Drinfeld V. Constant quasiclassical solutions of the Yang-Baxter quantum equation. Soviet Math Dokl, 1983, 28(3): 667--671
[3] Drinfeld V. Quantum groups. New York: Amer Math Society, 1987: 789--820
[4] Grunspan C. Quantizations of the Witt algebra and of simple Lie algebras in characteristic p. J Algebra, 2004, 280: 145--161
[5] Giaquinto A, Zhang J. Bialgebra action, twists and universal deformation formulas. J Pure Appl Algebra, 1998, 128(2): 133--151
[6] Hu N, Wang X. Quantizations of generalized-Witt algebra and of Jacobson-Witt algebra in modular case. J Algebra, 2007, 312: 902--929
[7] Michaelis W. A Class of infinite-dimensional Lie bialgebras containing the Virasoro algebras. Adv Math, 1994, 107: 365--392
[8] Ng S-H, Taft E J. Classification of the Lie bialgebra structures on the Witt and Virasoro algebras. J Pure Appl Algebra, 2000, 151: 67--88
[9] Shen R, Su Y. Classification of irreducible weight modules with finite-dimensional weight space over twisted
Heisenberg-Virasoro algebra. Acta Math Sinica (English Series), 2007, 23: 189--192
[10] Su Y. Quasifinite representations of a Lie algebra of Block type. J Algebra, 2004, 276: 117--128
[11] Song G, Su Y. Lie bialgebras of generalized Witt type. Science in China A, 2006, 49: 533-544
[12] Taft E J. Witt and Virasoro algebras as Lie bialgebras. J Pure Appl Algebra, 1993, 87: 301--312
[13] Xu X. New generalized simple Lie algebras of Cartan type over a field with characteristic 0. J Algebra, 2000, 224: 23--58
[14] Xu X. Quadratic conformal superalgebras.J Algebra, 2000, 231: 1--38
[15] Xu X. Generalizations of Block algebras. Manuscripta Math, 1999, 100: 489--518
[16] Wu Y, Song G, Su Y. Lie bialgebras of generalized Virasoro-like type. Acta Math Sinica (English Series), 2006, 22(6): 1915--1922
[17] Yue X, Su Y. Highest weight representations of a family of Lie algebras of Block type. Acta Math Sinica (English Series), 2008, 24(4): 687--696
/
| 〈 |
|
〉 |