Journal of Lie Theory 26 (2016), No. 3, 777--786
Copyright Heldermann Verlag 2016
Linear Commuting Maps and Biderivations on the Lie Algebras W(a,b)
Xiu Han
School of Math and Physical Science, Xuzhou Institute of Technology, Xuzhou 221008, P. R. China
xhan@xzit.edu.cn
Dengyin Wang
Dept. of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
Chunguang Xia
Dept. of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
chgxia@cumt.edu.cn
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).
Keywords: Biderivations, commuting maps, Lie algebra W(a,b).
MSC: 17B05, 17B40, 17B68
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