RESEARCH ARTICLE

Super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras

  • Zhuo ZHANG ,
  • Jixia YUAN ,
  • Xiaomin TANG
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  • School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China

Received date: 13 Oct 2020

Accepted date: 30 Nov 2020

Published date: 15 Dec 2020

Copyright

2020 Higher Education Press

Abstract

We mainly study the super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we prove that all super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras are inner.

Cite this article

Zhuo ZHANG , Jixia YUAN , Xiaomin TANG . Super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras[J]. Frontiers of Mathematics in China, 2020 , 15(6) : 1295 -1306 . DOI: 10.1007/s11464-020-0883-4

1
Brěsar M. On generalized biderivations and related maps. J Algebra, 1995, 172(3): 764–786

DOI

2
Chen Z X. Biderivations and linear commuting maps on simple generalized Witt algebras over a field. Electron J Linear Algebra, 2016, 31(1): 1–12

DOI

3
Cheng X, Wang M J, Sun J C, Zhang H L. Biderivations and linear commuting maps on the Lie algebras. Linear Multilinear Algebra, 2017, 65(12): 2483–2493

DOI

4
Du Y Q, Wang Y. Biderivations of generalized matrix algebras. Linear Algebra Appl, 2013, 438(11): 4483–4499

DOI

5
Fan G Z, Dai X S. Super-biderivations of Lie superalgebras. Linear Multilinear Algebra, 2017, 65(1): 58–66

DOI

6
Jiao Y, Liu W D. The derivations and the multiplicative Hom-structures of Filiform Lie Super-algebras Ln,m.Pure Appl Math, 2014, 30(5): 534–542

7
Kac V G. Lie superalgebras. Adv Math, 1977, 26: 8–96

DOI

8
Li J J, Fan G Z. Structures of not-finitely graded Lie superalgebras. J Gen Lie Theory Appl, 2016, 10(1): 5 papers

DOI

9
Li W H, Tang X M, Yuan J X. Super-biderivations and linear super-commuting maps on the super W-algebra W ˜(2, 2).Colloq Math, 2018, 153: 273–300

10
Liu X W, Guo X Q, Zhao K M. Biderivations of block Lie algebras. Linear Algebra Appl, 2018, 538(2): 43–55

DOI

11
Tang X M. Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras. Comm Algebra, 2017, 45(12): 5252–5261

DOI

12
Tang X M. Biderivations of finite-dimensional complex simple Lie algebra. Linear Multilinear Algebra, 2018, 66(2): 250–259

DOI

13
Wang D Y, Yu X X, Chen Z X. Biderivations of the parabolic subalgebras of simple Lie algebras. J Lie Theory, 2011, 39(11): 4097–4104

DOI

14
Xia C G, Han X, Wang D Y. Linear commuting maps and biderivations on Lie algebras W (a, b).J Lie Theory, 2016, 26(3): 777–786

15
Xia C G, Wang D Y, Han X. Linear super-commuting maps and super-biderivations on the super-Virasoro algebras. Comm Algebra, 2016, 44(12): 5342–5350

DOI

16
Yuan J X, Tang X M. Super-biderivations of classical simple Lie superalgebras. Aequationes Math, 2018, 92(1): 91–109

DOI

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