Linear super-commuting maps and super-biderivations on the super-Virasoro algebras. (English) Zbl 1380.17020
Summary: Let \(\mathrm{SVir}\) be the well-known super-Virasoro algebras. In this paper, we first prove that any super-skewsymmetric super-biderivation of \(\mathrm{SVir}\) is inner. Based on this, we show that every linear super-commuting map \(\psi\) on \(\mathrm{SVir}\) is of the form \(\psi (x)=f(x)c\), where \(f\) is a linear function from \(\mathrm{SVir}\) to \(\mathbb C\) mapping the odd part of \(\mathrm{SVir}\) to zero, and \(c\) is the central charge of \(\mathrm{SVir}\).
MSC:
| 17B68 | Virasoro and related algebras |
| 17B40 | Automorphisms, derivations, other operators for Lie algebras and super algebras |
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