Super-biderivations and linear super-commuting maps on infinite-dimensional Lie superalgebras

Let \mathcal{G}_{\epsilon} (resp. \mathcal{W}_{\epsilon}) with \epsilon=۰ or \frac{۱}{۲} be the complete spectrum-generating superalgebra (resp. the centerless super Virasoro algebra). In this paper, the super-skewsymmetric super-biderivations on \mathcal{G}_{\epsilon} and \mathcal{W}_{\epsilon} are completely determined. In particular, we show that every super-skewsymmetric super-biderivation \varphi (resp. \phi) of \mathcal{G}_{\epsilon} (resp. \mathcal{W}_{\epsilon}) is inner. Based on the results of super-biderivations, we shall give the certain forms of all linear super-commuting maps on \mathcal{G}_{\epsilon} and \mathcal{W}_{\epsilon}

کلیدواژه ها:

‎Complete spectrum-generating superalgebra ، Centerless super Virasoro algebra ، Super-biderivation ، Super-skewsymmetric ، Linear super-commuting map