Super-biderivations on twisted N = 1 Schrödinger-Neveu-Schwarz algebra

Abstract

Let \widetilde{tsns} denote the twisted N = 1 Schrodinger-Neveu-Schwarz algebra over the complex field ℂ. In this paper, we determine the superskewsymmetric super-biderivations of \widetilde{tsns}. Furthermore, we prove that every super-skewsymmetric super-biderivation of \widetilde{tsns} is inner.

Keywords

Lie super-algebra / super-biderivation / super-skewsymmetric

References

[1] Brešar M. On generalized biderivations and related maps. J Algebra, 1995, 172: 764–786

[2] Brešar M. Commuting maps: a survey. Taiwanese J Math, 2004, 8: 361–397

[3] Brešar M, Zhao K. Biderivations and commuting linear maps on Lie algebras. J Lie Theory, 2018, 28: 885–900

[4] Fa H, Li J, Zheng Y. Structures of the twisted N= 1 Schödinger-Neveu-Schwarz algebra. Comm Algebra, 2017, 45: 630–659

[5] Fan G, Dai X. Super-biderivations of Lie superalgebras. Linear Multilinear Algebra, 2017, 65: 58–66

[6] Han X, Wang D, Xia C. Linear commuting maps and biderivations on the Lie algebra W(a,b). J Lie Theory, 2016, 26(3): 777–786

[7] Wang D, Yu X. Biderivation and linear commuting maps on the Schrödinger-Virasoro Lie algebra. Comm Algebra, 2013, 41: 2166–2173

[8] Wang D, Yu X, Chen Z. Biderivations of the parabolic subalgebras of simple Lie algebras. Comm Algebra, 2011, 39: 4097–4104

[9] Xia C, Wang D, Han X. Linear super-commuting maps and super-biderivations on the super-Virasoro algebras. Comm Algebra, 2016, 44: 5342–5350

RIGHTS & PERMISSIONS

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature