Super-biderivations and linear super-commuting maps on the N=2 superconformal algebra

In this paper, we first determine all the super-skewsymmetric super-biderivations of the N=2 superconformal algebra $\mathfrak{g}$. As an application of super-biderivations, we give the explicit form of each linear super-commuting map on the N=2 superconformal algebra $\mathfrak{g}$. We prove that every super-biderivation of the N=2 superconformal algebra $\mathfrak{g}$ is inner, but the corresponding super-commuting maps are non-standard.

Keywords:

Lie super-algebra, super-biderivation super-skewsymmetric, linear super-commuting map,

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[1] M. Ademollo, L. Brink, A. d’Adda, R. Auria, E. Napolitano, S. Sciuto, E. del Giudice, P. di Vecchia, S. Ferrara, F. Gliozzi, R. Musto and R. Pettorino, Supersymmetric strings andcolour connement, Phys. Lett. B 62, 105-110, 1976.
[2] M. Brešar, On generalized biderivations and related maps, J. Algebra 172, 764-786, 1995.
[3] M. Brešar, Commuting maps: A survey, Taiwanese J. Math. 8, 361-397, 2004.
[4] G.-Z. Fan and X.-S. Dai, Super-biderivations of Lie superalgebras, Linear Multilinear Algebra 26 (1), 58-66, 2017.
[5] M. Fo˘sner, On the extended centroid of prime associative superalgebras with applications to superderivations, Commun. Algebra 32 , 689-705, 2004.
[6] X. Han, D.-Y. Wang and C.-G. Xia, Linear commuting maps and biderivations on the Lie algebra W(a,b), J. Lie theory 26 (3), 777-786, 2016.
[7] V. Kac, Lie superalgebras, Adv. Phys. 26, 8-96, 1977.
[8] D.-Y. Wang and X.-X. Yu, Biderivation and linear commuting maps on the Schrödinger-Virasoro Lie algebra, Comm. Algebra 41, 2166-2173, 2013.
[9] C.-G. Xia, D.-Y. Wang and X. Han, Linear super-commuting maps and superbiderivations on the super-Virasoro algebras, Comm. Algebra 44 (12), 5342-5350, 2016.

Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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