Second Leibniz cohomology group of twisted N = 2 superconformal algebra

Abstract

In this paper, we obtain all the Leibniz 2-cocycles of the twisted N = 2 superconformal algebra ℒ, which determine its second Leibniz cohomology group.

Keywords

Twisted N = 2 superconformal algebra / Leibniz 2-cocycle

References

[1.] Ademollo M., Brink L., d’Adda A., Auria R., Napolitano E., Sciuto S., del Giudice E., di Vecchia P., Ferrara S., Gliozzi F., Musto R., Pettorino R. Supersymmetric strings and colour confinement. Phys Lett B, 1976, 62: 105-110.

[2.] Dörrzapf M., Gato-Rivera B. Singular dimensions of the N = 2 superconformal algebras II: the twisted N = 2 algebra. Comm Math Phys, 2001, 220: 263-292.

[3.] Fu J., Jiang Q., Su Y. Classification of modules of the intermediate series over Ramond N = 2 superconformal algebras. J Math Phys, 2007, 48(043508): 1-15.

[4.] Hu N., Pei Y., Liu D. A cohomological characterization of Leibniz central extensions of Lie algebras. Proc Amer Math Soc, 2008, 136: 437-447.

[5.] Kac V. G. Lie superalgebras. Adv Math, 1977, 26: 8-97.

[6.] Kac V. G., van de Leuer J. W. On Classification of Superconformal Algebras, 1988, Singapore: World Scientific.

[7.] Li J., Su Y. Leibniz central extension on centerless twisted Schrödinger-Virasoro algebra. Front Math China, 2008, 3: 337-344.

[8.] Liu D., Hu N. Leibniz central extensions on some infinite-dimensional Lie algebras. Comm Alg, 2004, 6: 2385-2405.

[9.] Loday J. Cut-product for Leibniz cohomology and dual Leibniz algebras. Math Scand, 1995, 77: 189-196.

[10.] Loday J., Pirashvili T. Universal enveloping algebras of Leibniz algebras and (co)-homology. Math Ann, 1993, 296: 139-158.

[11.] Wang Q., Tan S. Leibniz central extension on a Block algebra. Alg Colloq, 2007, 4: 713-720.