Biderivations, commuting mappings and 2-local derivations of -graded Lie algebras of maximal class.

In Fialowski's classification for algebras of maximal class, there are three Lie algebras of maximal class with one-dimensional homogeneous components: $ \mathfrak {m}_0 $ m 0 , $ L_1 $ L 1 and $ \mathfrak {m}_2 $ m 2 . In this paper, we study their biderivations by considering the embedded mapping to derivation algebras. Then we determine commuting mappings on these algebras as an application of biderivations. Finally, local and 2-local derivations for these three algebras are characterized as the given gradings. [ABSTRACT FROM AUTHOR]