Abstract
Here, we investigate symmetric bi-derivations and their generalizations on L? 0 (G)*. For k ? N, we show that if B:L?0(G)*x L?0(G)* ? L?0(G)* is asymmetric bi-derivation such that [B(m,m),mk] ? Z(L?0(G)*) for all m ? L? 0 (G)*, then B is the zero map. Furthermore, we characterize symmetric generalized biderivations on group algebras. We also prove that any symmetric Jordan bi-derivation on L? 0(G)* is a symmetric bi-derivation.
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