Frontiers of Mathematics in China >

2022 , Vol. 17 >Issue 6: 1157 - 1167

DOI: https://doi.org/10.1007/s11464-021-0965-y

RESEARCH ARTICLE

Conformal biderivations of loop W (a, b) Lie conformal algebra

  • Jun ZHAO 1 ,
  • Liangyun CHEN , 1 ,
  • Lamei YUAN 2
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  • 1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
  • 2. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received date: 18 May 2020

Accepted date: 04 Aug 2021

Copyright

2022 Higher Education Press
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Abstract

We study conformal biderivations of a Lie conformal algebra. First, we give the definition of a conformal biderivation. Next, we determine the conformal biderivations of loop W(a, b) Lie conformal algebra, loop Virasoro Lie conformal algebra, and Virasoro Lie conformal algebra. Especially, all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.

Key words： Lie conformal algebras; conformal biderivations; Virasoro Lie conformal algebra; loop Virasoro Lie conformal algebra; loop W(a,b) Lie conformal algebra

Cite this article

Jun ZHAO , Liangyun CHEN , Lamei YUAN . Conformal biderivations of loop W (a, b) Lie conformal algebra[J]. Frontiers of Mathematics in China, 2022 , 17(6) : 1157 -1167 . DOI: 10.1007/s11464-021-0965-y

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Bakalov B , Kac V G , Voronov A A . Cohomology of conformal algebras. Comm Math Phys, 1999, 200 (3): 561- 598

2
Brešar M . Centralizing mappings and derivations in prime rings. J Algebra, 1993, 156 (2): 385- 394

3
Brešar M . Commuting maps: a survey. Taiwanese J Math, 2004, 8 (3): 361- 397

4
Brešar M , Zhao K M . Biderivations and commuting linear maps on Lie algebras. J Lie Theory, 2018, 28 (3): 885- 900

5
Chi L L , Sun J C , Yang H Y . Biderivations and linear commuting maps on the planar Galilean conformal algebra. Linear Multilinear Algebra, 2018, 66 (8): 1606- 1618

6
D’Andrea A , Kac V G . Structure theory of finite conformal algebras. Selecta Math (N S), 1998, 4 (3): 377- 418

7
Fan G Z , Wu H N , Yu B . Loop W(a, b) Lie conformal algebra. Internat J Math, 2016, 27 (2): 1650016 (13 pp)

8
Han X , Wang D Y , Xia C G . Linear commuting maps and biderivations on the Lie algebras W(a, b). J Lie Theory, 2016, 26 (3): 777- 786

9
Liu X , Guo X Q , Zhao K M . Biderivations of the block Lie algebras. Linear Algebra Appl, 2018, 538: 43- 55

10
Tang X M . Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras. Comm Algebra, 2017, 45 (12): 5252- 5261

11
Tang X M . Biderivations and commutative post-Lie algebra structures on the Lie algebra W(a, b). Taiwanese J Math, 2018, 22 (6): 1347- 1366

12
Wang D Y , Yu X X . Biderivations and linear commuting maps on the SchrödingerVirasoro Lie algebra. Comm Algebra, 2013, 41 (6): 2166- 2173

13
Wu H N , Chen Q F , Yue X Q . Loop Virasoro Lie conformal algebra. J Math Phys, 2014, 55 (1): 011706 (8 pp)

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