Skew-symmetric biderivations and linear commuting maps on the algebra SW(b)

For the parameter b is an element of C, denote the semi-direct product of the Witt algebra and the loop Schrodinger algebra as SW(b). In this paper, we investigate the skew-symmetric biderivations of this Lie algebra. As an application, we give the explicit form of each linear commuting map on SW(b). It turns out that on SW(b) we have only inner biderivations and standard linear commuting maps except in the case b=-12.