Please wait a minute...
Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

Postal Subscription Code 80-964

2018 Impact Factor: 0.565

Front. Math. China    2008, Vol. 3 Issue (3) : 337-344    https://doi.org/10.1007/s11464-008-0031-z
Leibniz central extension on centerless twisted Schr?dinger-Virasoro algebra
LI Junbo1, SU Yucai2
1.Department of Mathematics, Shanghai Jiao Tong University; Department ofMathematics, Changshu Institute of Technology; 2.Department of Mathematics, University of Science and Technology of China;
 Download: PDF(109 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract In this paper, we present all the Leibniz 2-cocycles of the centerless twisted Schrödinger-Virasoro algebra L, which determine the second Leibniz cohomology group of L.
Issue Date: 05 September 2008
 Cite this article:   
LI Junbo,SU Yucai. Leibniz central extension on centerless twisted Schr?dinger-Virasoro algebra[J]. Front. Math. China, 2008, 3(3): 337-344.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-008-0031-z
https://academic.hep.com.cn/fmc/EN/Y2008/V3/I3/337
1 Dokovic D, Zhao K . Derivations, isomorphismsand second cohomology of generalized Block algebras. Alg Colloq, 1996, 3: 245–272
2 Farnsteiner R . Derivationsand central extensions of finitely generated graded Lie algebra. J Algebra, 1988, 118: 33–45.
doi:10.1016/0021‐8693(88)90046‐4
3 Henkel M . Schrödingerinvariance and strongly anisotropic critical systems. J Stat Phys, 1994, 75: 1023–1029.
doi:10.1007/BF02186756
4 Henkel M . Phenomenologyof local scale invariance: from conformal invariance to dynamicalscaling. Nucl Phys B, 2002, 641: 405–410.
doi:10.1016/S0550‐3213(02)00540‐0
5 Henkel M, Unterberger J . Schrödinger invarianceand space-time symmetries. Nucl Phys B, 2003, 660: 407–412
6 Hilton P J, Stammbach U . A Course in Homological Algebra. 2nd ed. New York: Springer-Verlag, 1997
7 Hu N, Pei Y, Liu D . A cohomological characterization of Leibniz central extensionsof Lie algebras. Proc Amer Math Soc, 2008, 136: 437–447.
doi:10.1090/S0002‐9939‐07‐08985‐X
8 Kac V, Raina A . Bombay Lectures on HighestWeight Representations of Infinite Dimensional Lie Algebras. Singapore: World Scientific, 1987
9 Li J, Su Y . Representations of the Schrödinger-Virasoroalgebras. J Math Phys, 2008, 49(5): 053512.
doi: 10.1063/1.2924216
10 Liu D, Hu N . Leibniz central extensionson some infinite-dimensional Lie Algebras. Comm Alg, 2004, 6: 2385–2405.
doi:10.1081/AGB‐120037228
11 Loday J . Cut-productfor Leibniz cohomology and dual Leibniz algebras. Math Scand, 1995, 77: 189–196
12 Loday J, Pirashvili T . Universal enveloping algebrasof Leibniz algebras and (co)-homology. Math Ann, 1993, 296: 139–158.
doi:10.1007/BF01445099
13 Roger C, Unterberger J . The Schrödinger-VirasoroLie group and algebra: representation theory and cohomological study. Ann Henri Poincaré, 2006, 7: 1477–1529.
doi:10.1007/s00023‐006‐0289‐1
14 Su Y . Harish-Chandramodules of the intermediate series over the high rank Virasoro algebrasand high rank super-Virasoro algebras. J Math Phys, 1994, 35: 2013–2023.
doi:10.1063/1.530534
15 Su Y . Simplemodules over the high rank Virasoro algebras. Commun Alg, 2001, 29: 2067–2080.
doi:10.1081/AGB‐100002169
16 Su Y . Classificationof Harish-Chandra modules over the higher rank Virasoro algebras. Comm Math Phys, 2003, 240: 539–551
17 Su Y, Zhao K . Generalized Virasoro andsuper-Virasoro algebras and modules of intermediate series. J Algebra, 2002, 252: 1–19.
doi:10.1016/S0021‐8693(02)00021‐2
18 Wang Q, Tan S . Leibniz central extensionon a Block algebra. Alg Colloq, 2007, 4: 713–720
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed