
Journal of Lie Theory 26 (2016), No. 3, 777786 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 skewsymmetric 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 noninner biderivations and nonstandard linear commuting maps for certain W(a,b). Keywords: Biderivations, commuting maps, Lie algebra W(a,b). MSC: 17B05, 17B40, 17B68 [ Fulltextpdf (248 KB)] for subscribers only. 