Journal of Lie Theory

no. 3
Linear Commuting Maps and Biderivations on the Lie Algebras W(a,b)
Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 777-786
Let W(a,b) be the semidirect product Lie algebra of the centerless Virasoro algebra and its module of the intermediate series, where a,b are elements of C. In this paper, we first determine all the skew-symmetric biderivations of W(a,b). Based on the result of biderivations, we give the explicit form of each linear commuting map on W(a,b). In particular, we find that there exist non-inner biderivations and non-standard linear commuting maps for certain W(a,b).
DOI: 10.5802/jolt.912
Classification: 17B05, 17B40, 17B68
Keywords: Biderivations, commuting maps, Lie algebra W(a,b) 
@article{JOLT_2016_26_3_a10,
     author = {X. Han and D. Wang and C. Xia},
     title = {Linear {Commuting} {Maps} and {Biderivations} on the {Lie} {Algebras} {W(a,b)}},
     journal = {Journal of Lie Theory},
     pages = {777--786},
     year = {2016},
     volume = {26},
     number = {3},
     doi = {10.5802/jolt.912},
     zbl = {1406.17034},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.912/}
}
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X. Han; D. Wang; C. Xia. Linear Commuting Maps and Biderivations on the Lie Algebras W(a,b). Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 777-786. doi: 10.5802/jolt.912

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